Determining the sin theta, tan theta and cos theta at P (x,y)

[Tazook]

Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position.
(b) (3, 4) ( (d) (12, 5)
(f) (7, 24)
for b I was able to do
tan \theta= y/x
tan \theta= 4/3
\theta = 53.13
My textbook says I am wrong... doing an online course... teacher is so lazy that she never posted how to do it but rather read txtbook pg... Did not help...

 

[skeeter]

Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position.
(b) (3, 4) ( (d) (12, 5)
(f) (7, 24)
for b I was able to do
tan \theta= y/x
tan \theta= 4/3
\theta = 53.13
My textbook says I am wrong... doing an online course... teacher is so lazy that she never posted how to do it but rather read txtbook pg... Did not help...

\(\displaystyle \sin{\theta} = \frac{y}{\sqrt{x^2+y^2}}\)

\(\displaystyle \tan{\theta} = \frac{y}{x}\)

\(\displaystyle \cos{\theta} = \frac{x}{\sqrt{x^2+y^2}}\)

 

[Amad27]

Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position.
(b) (3, 4) ( (d) (12, 5)
(f) (7, 24)
for b I was able to do
tan \theta= y/x
tan \theta= 4/3
\theta = 53.13
My textbook says I am wrong... doing an online course... teacher is so lazy that she never posted how to do it but rather read txtbook pg... Did not help...

Ah -- I see your trouble here. What you have should be almost correct.

What skeeter recommended is what you (sort of) did.

You are right that $\theta = 53.13$ degrees.

But the question is not asking you to find $\theta$ but the values of $\sin \tan \cos$ at the value of $v = \theta$

In my point of view,

$\tan(\theta) = \frac{4}{3}$ is indeed correct because you correctly did

$\tan(\theta) = y/x$ but instead you took $\arctan(y/x)$ instead of giving $\tan(\theta)$