Download π 2. sin60 cos45 o − cos60 sin45 π β

PRECALCULUS HONORS TEST REVIEW
5.4—5.5
Find the exact value of the sine, cosine, and tangent of the angle by using a sum or difference
formula.
1.
25π 11π π
=
+
12
6
4
Write the expression as the sine, cosine, or tangent of an angle.
2. sin60o cos 45o − cos60osin 45o
Find the exact value of the trigonometric function given that sin u =
(Both u and v are in Quadrant II.)
3. sin(u − v)
3
5
and cos v = − .
4
13
4. tan(u + v)
Verify the identity.
⎛π
⎞
5. cot ⎜ − x ⎟ = tan x
⎝2
⎠
6.
sin(α + β )
= tan α + tan β
cos α cos β
Find all solutions of the equation in the interval [0, 2π).
π⎞
π⎞
⎛
⎛
7. sin ⎜ x + ⎟ − sin ⎜ x − ⎟ = 1
⎝
⎝
6⎠
6⎠
Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.
8. cosu = −
2 π
,
<u <π
5 2
Use double-angle formulas to verify the identity algebraically.
9. sin 4x = 8cos3 xsin x − 4 cos xsin x
Use the power-reducing formulas to rewrite the expression in terms of the first power of the
cosine.
10. cos2 3x
11. sin2 x tan2 x
Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of
the angle.
12. 15o
Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.
2
13. cosu = − ,
7
π
2
<u <π
Use the half-angle formulas to simplify the expression.
14.
sin 6x
1 + cos 6x
Use the product-to-sum formulas to write the product as a sum or difference.
π
π
15. 3cos sin
6
6
Use the sum-to-product formulas to write the sum or difference as a product.
π⎞
π⎞
⎛
⎛
16. cos ⎜ x + ⎟ − cos ⎜ x − ⎟
⎝
⎝
4⎠
4⎠
17. A baseball leaves the hand of the person at first base at an angle of θ with the horizontal
and at an initial velocity of v0 = 80 feet per second. The ball is caught by the person at
1 2
second base 100 feet away. Find θ if the range r of a projectile is r =
v0 sin 2θ .
32
18. Determine whether the statement is true or false. Justify your answer.
sin(x + y) = sin x + sin y .