5.4 Tangent, Cotangent, Secant, Cosecant
5.4 Tangent, Cotangent, Secant, Cosecant
5.4 Tangent, Cotangent, Secant, Cosecant
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<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong><br />
Part 1<br />
Evaluate without using a calculator. Give exact values.<br />
<br />
π<br />
1. tan =<br />
6<br />
y 1/2<br />
= √ =<br />
x 3/2 1<br />
√<br />
3<br />
√ =<br />
3 3<br />
2. sec<br />
<br />
π<br />
=<br />
4<br />
1<br />
x<br />
= 1<br />
√ 2/2 = 2<br />
√ 2 = √ 2<br />
1
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
3. csc<br />
4. tan<br />
5. sec<br />
<br />
π<br />
=<br />
3<br />
1<br />
y<br />
<br />
2π<br />
=<br />
3<br />
y<br />
x =<br />
<br />
5π<br />
=<br />
6<br />
1<br />
x =<br />
= 1<br />
√ 3/2 = 2<br />
√ 3 = 2√ 3<br />
3<br />
√ 3/2<br />
−1/2 = −√ 3<br />
1<br />
− √ 3/2<br />
= − 2<br />
√ 3 = − 2√ 3<br />
3<br />
2
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
6. csc<br />
7. tan<br />
<br />
5π<br />
=<br />
3<br />
1<br />
y =<br />
1<br />
− √ 3/2<br />
<br />
5π<br />
=<br />
4<br />
y<br />
x = −√2/2 − √ 2/2<br />
<br />
11π<br />
8. sec<br />
6<br />
= 1<br />
x<br />
= − 2<br />
√ 3 = − 2√ 3<br />
3<br />
= 1<br />
= 1<br />
√ 3/2 = 2<br />
√ 3 = 2√ 3<br />
3<br />
3
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
9. tan<br />
10. csc<br />
<br />
2π<br />
=<br />
3<br />
y<br />
x = −√3/2 1/2 = −√3 <br />
7π<br />
=<br />
6<br />
1<br />
y<br />
= 1<br />
−1/2<br />
= −2<br />
4
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
Part 2<br />
Sketch the graph of the function over a two period interval.<br />
1. y = tan 4x<br />
2. y = 3 tan x<br />
3. y = tan 2x<br />
5
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
4. y = tan 1<br />
4 x<br />
5. y = tan <br />
x − π<br />
<br />
6. y = tan <br />
x + π<br />
<br />
2<br />
4<br />
6
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
7. y = − tan x<br />
8. y = − tan <br />
x − π<br />
<br />
9. y = 2 cot x<br />
2<br />
7
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
10. y = cot 2x<br />
11. y = cot 1<br />
2 x<br />
12. y = csc x<br />
8
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
13. y = csc(2x)<br />
14. y = csc <br />
x − π<br />
<br />
15. y = sec x<br />
4<br />
9
<strong>5.4</strong> <strong>Tangent</strong>, <strong>Cotangent</strong>, <strong>Secant</strong>, <strong>Cosecant</strong> Math 170 Homework Solutions<br />
16. y = sec 1<br />
2 x<br />
10
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