UCR MATH 8B-030 FALL 2014
HOMEWORK
Homework 3: Due Wednesday 10/22/14
Inverse Trig Functions.
1. Find the exact value of the the following or state that it is undefined;
a. arcsin − 12 .
√
b. arccos 22 .
c. arctan √13 .
d. arcsin π2 .
2. Find the exact value of the following;
a. cos arcsin 23 , b. sin arccos − 45 ,
c. tan arcsin − 43 ,
d. sin(arctan(4)).
3. Find an equivalent algebraic expression for the following;
a.
b.
c.
d.
cos(arctan(x)),
tan(arcsin(x)), |x| < 1,
tan(arccos(x)), |x| ≤ 1, x 6= 0,
sin(arccos(x)), |x| ≤ 1.
Trig Equations.
4. Find all solutions to the following equations, express your answers in radians;
√
a. sin(x) =
2
.
2
√
b. cos(x) = −
3
.
2
√
c. tan(x) = − 3.
5. Find all solutions to the following equation,
a. 2 sin(θ) + 3 = 2
b. tan(2θ) = −1
Last updated: October 19, 2014.
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UCR MATH 8B-030 FALL 2014 HOMEWORK
c. sin(2x) =
1
2
d. 2 sin x −
π
4
+1=2
e. 2 cos2 (θ) + cos(θ) = 0
f. 2 sin2 (θ) − 5 sin(θ) + 3 = 0
g. sin2 (θ) − cos2 (θ) = 1 + cos(θ)
Verifying Identities.
6. Verify the following identities;
cot(x)
a. csc(x)−1
= csc(x)+1
cot(x)
b. sec2 (x) − csc2 (x) =
1
1+sin(x)
tan(x)−cot(x)
sin(x) cos(x)
c.
1
1−sin(x)
+
d.
sin(x)
1+cos(x)
= csc(x) − cot(x)
e.
sin(x)+tan(x)
cos(x)+1
= 2 sec2 (x)
= tan(x)