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IB Math SL1/Intensified Precalculus
Name
10.J Worksheet
For 1 and 2: Use an angle sum or difference identity to find the exact value of each.
1.
sin
5π
12
(
2. cos −15o
)
For 3 and 4: Use a double-angle identity to find the exact value of each expression.
3. sin
5π
12
5. Given sin θ =
4. tan195o
7
π
and < θ < π . Find: sin 2θ
25
2
3
6. Given sin θ = − and 180o < θ < 270o . Find: tan 2θ
5
7. Given cos 2θ =
10
π
and 0 < 2θ < . Find: csc θ
10
2
7π
⎛
8. Solve the equation for −π ≤ θ ≤ π : −5 − 4 cos ⎜ −4θ +
4
⎝
⎞
⎟ = −2 3 − 5
⎠
For 9 and 10: Find the exact value of the following given that sin x =
5
3
, cos y = − where
13
5
both x and y are in quadrant 2.
9. sin ( x + y )
10. cos ( y − x )
ANSWER KEY
1.
2.
3.
6+ 2
4
6+ 2
4
1
3
+
2 4
2− 3
2+ 3
336
5. −
625
4.
6.
24
7
7.
20
10 − 10
29π 25π 5π
π 19π 23π 43π 47π
,−
,− ,− ,
,
,
,
48
48
48 48 48 48 48 48
63
9. −
65
56
10.
65
8. −