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Answer:
Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
cos
(
θ
)
=
adjacent
hypotenuse
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Opposite
=
√
hypotenuse
2
−
adjacent
2
Replace the known values in the equation.
Opposite
=
√
(
17
)
2
−
(
15
)
2
Simplify
√
(
17
)
2
−
(
15
)
2
.
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Opposite
=
8
Find the value of sine.
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sin
(
θ
)
=
8
17
Find the value of tangent.
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tan
(
θ
)
=
8
15
Find the value of cotangent.
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cot
(
θ
)
=
15
8
Find the value of secant.
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sec
(
θ
)
=
17
15
Find the value of cosecant.
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csc
(
θ
)
=
17
8
This is the solution to each trig value.
sin
(
θ
)
=
8
17
cos
(
θ
)
=
15
17
tan
(
θ
)
=
8
15
cot
(
θ
)
=
15
8
sec
(
θ
)
=
17
15
csc
(
θ
)
=
17
8