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Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.2: Verifying Trigonometric Identities

Problem 26E

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Verifying a Trigonometric Identity In Exercises 49-60
verify the identity algebraically. Use a graphing utility to
check your result graphically.
49. 2 sec² x − 2 sec² x sin² x − sin² x − cos²x = 1
53. sec 0 cot = csc 0

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Verifying a Trigonometric IdentityIn Exercises 19–24, verify the identityalgebraically. Use the table feature ofa graphing utility to check your resultnumerically.
Proof Use the trigonometric identitycos2 x + sin2 x = 1 to prove that (Hint: Beginby multiplying the numerator and denominator by cos x + 1.)
Verification of Trigonometric Identities
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Think About It In Exercises 67–70, explain why theequation is not an identity and find one value of thevariable for which the equation is not true.67. sin θ = √1 − cos2 θ 68. tan θ = √sec2 θ − 169. 1 − cos θ = sin θ 70. 1 + tan θ = sec θ
Verify the identity algebraically. Use the table feature of a graphing utility to check your result numerically. (Simplify at each step.) 6 cos(x) − 6 cos(x) 1 − tan(x) = 6 sin(x) cos(x) sin(x) − cos(x)
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Using a Calculator In Exercises 75–90,use a calculator to evaluate the trigonometricfunction. Round your answer to four decimalplaces. (Be sure the calculator is in thecorrect mode.)75. sin 10° 76. tan 304°77. cos(−110°) 78. sin(−330°)79. cot 178° 80. sec 72°81. csc 405° 82. cot(−560°)83. tanπ9 84. cos2π785. sec11π8 86. csc15π487. sin(−0.65) 88. cos 1.3589. csc(−10) 90. sec(−4.6)
Evaluating Trigonometric FunctionsIn Exercises 5–10, find the exact values of thesix trigonometric functions of the angle θ.
(cot β-tan β) • sin2 β
Evaluating an Inverse TrigonometricFunction In Exercises 5–18, find the exactvalue of the expression, if possible.

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