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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Use a calculator to evaluate the given expressions.tan−1(−2.8229)
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. sin (120° x) = V3cosx + sinx 2
Prove the given identities. cos 0 2 sin 0 2sin
Simplify the given expressions. cos3x sinx sin 3x COSX
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.2 sin x = tan x
Use a calculator to evaluate the given expressions.cos−1(−0.6561)
Prove the given identities.sin y + sin y cot2 y = csc y
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. tan (¹ + x) tanx − 1 tanx +1
Prove the given identities. X 2cos 2 = (1 + cosx)sec* 2
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.cos2x + sin2 x = 0
Use a calculator to evaluate the given expressions.sin−1 0.0219
Evaluate the given expressions.sin−1(−1)
Prove the given identities. cos? 1 + sinx 1+ cosx = 1
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. cos(x) = sin.x
Prove the given identities.cos2 α − sin2 α = 2cos2 α − 1
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.sin2 x − 2 sin x = 1
Use a calculator to evaluate the given expressions.cot−1 0.2846
Evaluate the given expressions.sec−1√2
Prove the given identities. cosx — tanxsinx sec.x cos2x
Prove the given identities.tan x + cot x = tan x csc2 x
Derive the given equations as indicated. Equations (20.14)–(20.16) are known as the product formulas.By dividing the right side of Eq. (20.9) by that of Eq. (20.10), and dividing the right side of
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. 2 sin ²-cos² = 2 2 1- 3 cosa 2
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.2 cos2 2x + 1 = 3 cos 2x
Use a calculator to evaluate the given expressions.tan[cos−1(−0.6281)]
Derive the given equations as indicated. Equations (20.14)–(20.16) are known as the product formulas.By adding Eqs. (20.9) and (20.11), derive the equation sina cos3 = [sin(a + 3) + sin(a -
Evaluate the given expressions.cos−1 0.8629
Prove the given identities.cos2 x − sin2 x = 1 − 2sin2 x
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. cos² A 2 sin 2. 2 sin 2A 2 sin A
Prove the given identities. 1+cosx sin x sin x 1 – cost
Prove the given identities. 2+ cos 20 sin ²0 csc ²0
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.tan x + 3 cot x = 4
Derive the given equations as indicated. Equations (20.14)–(20.16) are known as the product formulas.By adding Eqs. (20.10) and (20.12), derive the equation cos a cos 3 = [cos(a + 3) + cos(a −
Use a calculator to evaluate the given expressions.cos[tan(−7.2256)]
Evaluate the given expressions.tan−1(−6.249)
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. 2 sin² 0 2 sin ²0 1 + cos 0
Prove the given identities. sin 0 csc cose sec 0 = 1
Prove the given identities. sec cose tan 0 cot = 1
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.tan2 x + 4 = 2 sec2 x
Derive the given equations as indicated. Equations (20.14)–(20.16) are known as the product formulas.By subtracting Eq. (20.10) from Eq. (20.12), derive sinasin 3 = [cos(a - 3) - cos(a + 3)] (20.16)
Use a calculator to evaluate the given expressions.sin[tan−1(−0.2297)]
Evaluate the given expressions.tan[sin−1(−0.5)]
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. tan sina 1 + cosa
Prove the given identities. 2 tana 1 + tan² a sin 2a
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.sin 2x + cos2x = 0
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.2 sin 4x + csc 4x = 3
Derive the given equations by letting α + β = x and α − β = y, which leads to α = 1/2(x + y) and β = 1/2(x − y). The resulting equations are known as the factor formulas.Use Eq. (20.14) and
Use a calculator to evaluate the given expressions.tan[sin−1(−0.3019)]
Prove the given identities. 1- cos 20 2 1 + cot²0
Evaluate the given expressions.cos[tan−1(−√3)]
Prove the given identities. sin²0+ 2 cos 1 sin ²0+ 3cos0 - 3 1 1 - sec 0
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.2 sin 2x − cos x sin3 x = 0
Solve the given equations for x.y = sin3x
Derive the given equations by letting α + β = x and α − β = y, which leads to α = 1/2(x + y) and β = 1/2(x − y). The resulting equations are known as the factor formulas.Use Eqs. (20.9) and
Prove the given identities. cos³0 + sin ³0 cose + sin = 1 - --sin 20
Evaluate the given expressions.sin−1[cos(7π/6)]
In a right triangle with sides and angles as shown in Fig. 20.22, show that sin 24 2 C - b 2c
Prove the given identities.2sin4 x − 3sin2 x + 1 = cos 2 x(1 − 2sin2 x)
Find tanθ if sin(θ/2) = 3/5.
Solve the given trigonometric equations analytically and by use of a calculator. Compare results. Use values of x for 0 ≤ x < 2π.sec4 x = csc4 x
Derive the given equations by letting α + β = x and α − β = y, which leads to α = 1/2(x + y) and β = 1/2(x − y). The resulting equations are known as the factor formulas.Use Eq. (20.15) and
Solve the given equations for x.y = cos(2x − π)
Simplify the given expressions. sec y cos y tan y cot y
Evaluate the given expressions.cos−1[cot(−π/4)]
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. tan.x csc ² x 2 1 + tan² x
Solve the given equations for x.y = tan−1(x/4)
Simplify the given expressions. sin 20 2csc0 cos ³0
Solve the indicated equations analytically.sin 3x + sin x = 0
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. cosx - cos³x sinx − sin3 x
Prove the given identities.ln(1 − cos2x) − ln(1 + cos2x) = 2ln tan x
Find the exact value of tan 22.5° using half-angle formulas.
Solve the given equations for x.5y = 2 sin−1(x/6)
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. tan 20 2 cot tan0
Solve the indicated equations analytically.cos 3x − cos x = 0
Prove the given identities.log(20sin2 θ + 10 cos2θ) = 1
Use the half-angle formulas to solve the given problems.If 180° < θ < 270° and tan (θ/2) = −π/3, find sinθ.
Solve the given equations for x.1 − y = cos−1(1 − x)
Simplify the given expressions.sin x(csc x− sin x)
Is there any positive acute angle θ for which sinθ + cosθ + tanθ + cotθ + secθ + cscθ = 1? Explain.
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x.cot x(sec x − cos x)
Evaluate exactly: sin(x + 30°) cos x − cos(x + 30°) sin x
Simplify it : sin (0) + cos(-0)
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator. 1 - tan²x sec ² x cos2x
Find the area of the segment of the circle in Fig. 20.23, expressing the result in terms of θ/2.Fig. 20.23. 0 r
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. tanx cotx CSC X
Use the half-angle formulas to solve the given problems.If 90° < θ < 180° and sinθ = 4/5, find cos(θ/2).
Simplify the given expressions.cos y(sec y− cos y)
Prove the given identities. sec4 x 1 2 tan ² x 2 + tan² x
Solve the given equations for x.2y = cot−13x − 5
In finding the path of a sliding particle, the expressionis used. Simplify this expression. √8 - 8 cose
Use a calculator to determine the minimum value of the function to the left of the equal sign in Exercise 41 (for a positive acute angle).Data from exercises 41Is there any positive acute angle θ
Prove the given identities. cos² y sin² y - 1 tan² y 1 + tan² y
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x.sin x(tan x + cot x)
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. 1+tanx sinx sec.x
Find an algebraic expression for each of the given expressions.tan(sin−1 x)
Show that sin2 x/sin x = 2cos x
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator.(sin x + cos x)2 = 1 + sin 2x
Find an algebraic expression for each of the given expressions.sin(cos−1 x)
Solve the system of equations r = sinθ, r = cos 2θ, for 0 ≤ θ < 2π.
Simplify the given expressions. The result will be one of sin x, cos x, tan x, cot x, sec x, or csc x. cosx + sinx 1+tanx
Verify each identity by comparing the graph of the left side with the graph of the right side on a calculator.2csc2x tan x = sec2 x

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