(Solved) How do you find five other trigonometric function values?

bufi

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10 years ago

How do you find five other trigonometric function values?

If it is given that sin(theta)= -9/SqRt(97) and the terminal side is in quadrant III, how do you find the other five values (e.g. sec, cos, cot...)

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leejiawen

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10 years ago

You resolve the vector into components

Opposite

Adjacent

Hpyotenuse

Its super easy. Since they gave you Sine, then you already know O/H

Quandrant III means it is between 180-270 degrees ( or pi - 3pi/2 ) if in radians.

Sin = o/h
Cos = a/h
Tan = o/a
Csc = h/o
Sec = h/a
Cot = a/o

Trigonometry is like getting chance for a $20 bill in mexico.

If you know the ratio between their different denominations of currency, you can sorta guess how much to expect if you "get change for $100"

Hope this helps, and in mexico, they do actually use trigonometry at the airport and at customs.

Especially after all the beefed up security.

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lee628

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10 years ago

If that is the value of sin(theta), then csc(theta)=1/-9/Sq.Rt(97)= -Sq.Rt.(97)/9
By the Pythagorean theorem and since you already have the opposite side and the hypotenuse, you get that the adjacent side is -4(because it is in quadrant III).
cos(theta)= -4/Sq.Rt(97)
tan(theta)= 9/4
sec(theta)= -1/ 4/Sq.Rt(97)= -Sq.Rt(97)/4
cot(theta)=4/9

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buildmscl

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10 years ago

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darkp0tat0

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10 years ago

First, draw a diagram representing the X and Y coordinates and label the upper right quadrant as 1, the upper left as 2, the lower left as 3, and the lower right as 4.

The sin function is the side opposite the angle over the hypotenus. In our example, sin(theta)= -9/SqRt(97). The terminal side ends in quadrant 3. Draw a triangle with the origin as one point, and the other angle ending 9 spaces below the y axis. The triangle is a right triangle so the third angle is perpendicular to the y axis. Now solve for the length along the y axis from the origin using Pathagorem Theorem, x sq + y sq= z sq where x and y are the sides of the triangle and z is the hypotenueus. You will find the other side is -4, minus because it is to the left of the origin and -9 is negative because it is below tyhe origin.

Sin(theta)= side opposite/hypoteneus=-9/SqRt(97).

Cos(theta) = side adjacent/hypotenus which is -4/SqRt(97).

Tan(theta)= side opposite/side adjacent= -9/-4=2 and 1/4.

Cot(theta)= side adj/side opposite=-4/-9.

Sec(theta)= 1/cos(theta)=1/(-4/SqRt(97)).

Csc(theta)= 1/sin(theta)=1/(-9/SqRt(97)).

Be careful you use the correct signs, either positive or negative.

I hope that helps and you learn how to solve these problems by first drawing a diagram depicting the problem and known quantities.

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