PreCalculus 89-R 8 – Solving Trig Equations 9 – Trig Identities and Proof Review Problems
Simplify the following trigonometric expressions tan x 1 sin 2 x
Review Problems tan x cos x csc x 1 sin(z) + cos(–z) + sin(–z) cos z Simplify the following trigonometric expressions 2
Review Problems 1 Simplify the following trigonometric expressions cos B + sin B tan B sec B 3
Review Problems cos 2 x Simplify the following trigonometric expressions (1 – cos 2 x)(1 + cot 2 x) 1 4
Review Problems sin 2 t + cos 2 t + tan 2 t sec 2 t Simplify the following trigonometric expressions sec A 5
Review Problems 2 csc x Simplify the following trigonometric expressions cot x 6
Review Problems sin 2 x Simplify the following trigonometric expressions tan 2 t 7
Review Problems find the exact value of the expression. 8
Review Problems Write the expression as a trigonometric function of one number. 9
Review Problems Simplify the following expressions as much as possible. cot(x) cos(p + z) – cos(p – z)–2sin(p)sin(z) 10
Review Problems tan z Simplify the following expressions as much as possible. 0 11
Review Problems Write the following expression in terms of sine only. sin z + cos z 12
Review Problems Find the exact value of the expression. 13
Review Problems Evaluate the expressions by sketching a triangle 0 14
Review Problems Rewrite the expressions as an algebraic expression in x. tan (sin – 1 x) sin (2 cos – 1 x) cos (sin – 1 x + cos – 1 x) 0 15
Review Problems Find all solutions of the following equations. 16
Review Problems Find all solutions of the following equations. 4 cos 2 x – 4 cos x + 1 = 0 17
Review Problems cos 2 4 x – sin 2 4 x = 0 Find all solutions of the following equations. 2 cos x cot x – cot x = 1 – 2 cos x 18
Review Problems Find all solutions of the following equation in the interval. tan x – 3 cot x = 0 Find all solutions of the following equation in the interval. cos x cos 7 x – sin x sin 7 x = 0 19
Review Problems Simplify completely the trigonometric expressions
Review Problems 1 Simplify completely the trigonometric expressions 21
Review Problems Simplify completely the trigonometric expressions 22
Review Problems Simplify completely the trigonometric expressions 23
Review Problems Simplify completely the trigonometric expressions 24
Review Problems Simplify completely the trigonometric expressions 25
Review Problems Simplify completely the trigonometric expressions 26
Review Problems Find the exact value of the expressions 27
Review Problems Simplify completely the trigonometric expressions 28
Review Problems Simplify completely the trigonometric expressions 29
Review Problems Simplify completely the trigonometric expressions 30
Review Problems Use an appropriate half-angle formula to find the exact value of the expression. 31
Review Problems Use an appropriate half-angle formula to find the exact value of the expression. 32
Review Problems Write the products as a sum. 33
Review Problems Write the sum as a product. 34
Review Problems Find the value of the product. Find the value of the sum. 35
Review Problems Simplify the expressions. 36
Review Problems Simplify the expressions. 37
Review Problems Find all solutions of the equation. 38
Review Problems Find all solutions of the equation. 39
Review Problems Find all solutions of the equation. 40
Review Problems Find all solutions of the equation. 41
Review Problems Find all solutions of the equation. 42
Review Problems Find all solutions of the equation. 43
Review Problems Solve the equation by first using a sum-to-product formula 44
Review Problems Find the exact value for each trigonometric function. sec 120° tan 390° cos 315° –2 45
Review Problems Find the exact value of the expressions. 46
Review Problems Find the exact value of the expressions. 47
Review Problems Find the exact value of the expressions. 48
Review Problems Evaluate the expressions by sketching a triangle. 49
Review Problems 0 Evaluate the expressions by sketching a triangle. 50
Review Problems Rewrite the expression as an algebraic expression in x. sin (cos – 1 x) tan (sin – 1 x) 51
Review Problems Verify the identity 52
Review Problems Verify the identity 53
Review Problems Verify the identity 54
Review Problems Verify the identity 55
Review Problems Verify the identity 56
Review Problems Find all real solutions, to four decimal places 57
Review Problems Find all real solutions, to two decimal places 58
Answers tan x sin 2 x 1cos z 1sec B cos 2 x1 sec 2 tsec A 2 csc x cot x sin 2 xtan 2 t cot(x)–2sin(p)sin(z) tan z 0 0 0
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