Page 27 - Ebook Trigonometri_Krisna Hasugian_MESP 2019
P. 27
Example 20) sin 54° = cos 36°
How can we use these identities to find exact values of trigonometric functions?
Follow these examples to find out! Examples 21-26
21) Find the exact value of the expression
sin² 30° + cos² 30°
Solution: Since sin² + cos² = 1, therefore sin² 30° + cos² 30° = 1
22) Find the exact value of the expression
sin 45°
tan 45° −
cos 45°
sin 45°
Solution: Since ( ) = tan 45°, therefore tan 45° − tan 45° = 0
cos 45°
23) tan 35° ⋅ cos 35° ⋅ csc 35°
sin 35° cos 35° 1
Solution: ⋅ ⋅ = 1
cos 35° 1 sin 35°
24) tan 22° − cot 68°
Solution: tan 22° = cot 68°, therefore cot 68° − cot 68° = 0
2
25) cot = − , find csc , where is in quadrant II
3
Solution: Pick an identity that relates cotangent to cosecant, like the
Pythagorean identity 1 + cot² = csc² .
2 2
1 + (− ) = csc² θ
3
4
1 + = csc²
9
13 = csc²
9
√ = csc
13
9
√13
= csc
3
The positive square root is chosen because csc is positive in quadrant II
26
