if coso =35/37 find sing $ tano
Answers
Explanation:
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Trigonometry Examples
Popular Problems Trigonometry Find the Other Trig Values in Quadrant II sin(x)=35/37
sin
(
x
)
=
35
37
Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
sin
(
x
)
=
opposite
hypotenuse
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Adjacent
=
−
√
hypotenuse
2
−
opposite
2
Replace the known values in the equation.
Adjacent
=
−
√
(
37
)
2
−
(
35
)
2
Simplify
−
√
(
37
)
2
−
(
35
)
2
.
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Raise
37
to the power of
2
.
Adjacent
=
−
√
1369
−
(
35
)
2
Raise
35
to the power of
2
.
Adjacent
=
−
√
1369
−
1
⋅
1225
Multiply
−
1
by
1225
.
Adjacent
=
−
√
1369
−
1225
Subtract
1225
from
1369
.
Adjacent
=
−
√
144
Rewrite
144
as
12
2
.
Adjacent
=
−
√
12
2
Multiply.
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Pull terms out from under the radical, assuming positive real numbers.
Adjacent
=
−
1
⋅
12
Multiply
−
1
by
12
.
Adjacent
=
−
12
Find the value of cosine.
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Use the definition of cosine to find the value of
cos
(
x
)
.
cos
(
x
)
=
adj
hyp
Substitute in the known values.
cos
(
x
)
=
−
12
37
Move the negative in front of the fraction.
cos
(
x
)
=
−
12
37
Find the value of tangent.
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Use the definition of tangent to find the value of
tan
(
x
)
.
tan
(
x
)
=
opp
adj
Substitute in the known values.
tan
(
x
)
=
35
−
12
Move the negative in front of the fraction.
tan
(
x
)
=
−
35
12
Find the value of cotangent.
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Use the definition of cotangent to find the value of
cot
(
x
)
.
cot
(
x
)
=
adj
opp
Substitute in the known values.
cot
(
x
)
=
−
12
35
Move the negative in front of the fraction.
cot
(
x
)
=
−
12
35
Find the value of secant.
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Use the definition of secant to find the value of
sec
(
x
)
.
sec
(
x
)
=
hyp
adj
Substitute in the known values.
sec
(
x
)
=
37
−
12
Move the negative in front of the fraction.
sec
(
x
)
=
−
37
12
Find the value of cosecant.
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Use the definition of cosecant to find the value of
csc
(
x
)
.
csc
(
x
)
=
hyp
opp
Substitute in the known values.
csc
(
x
)
=
37
35
This is the solution to each trig value.
sin
(
x
)
=
35
37
cos
(
x
)
=
−
12
37
tan
(
x
)
=
−
35
12
cot
(
x
)
=
−
12
35
sec
(
x
)
=
−
37
12
csc
(
x
)
=
37
35