Question

Write the first trigonometric function in terms of the second for θ in the given quadrant.
cos θ, sin θ; θ in quadrant II

Answer 1

Do you know the definitions of sin in relation to cos and tan in relation to cot and then sec in relation to csc and cot in relation to tan?

Answer 2

I know that the second set are inverses. I am doing practice problems for pre calc summer school but i have no idea what i am doing

Answer 3

hey i appreciate that! thanks!! how do i express this in terms of the second quadrant?

Answer 4

Now all you have to is find the equation from sin, since they said they want you to write cos in terms of sin

Answer 5

Well since it's in the 2nd quadrant and the x points will be cos(theta) and y points will be sin(theta) (from the unit circle the signs of the points in the QII will be

Answer 6

-cos, +sin

Answer 7

oh sweet!! so for the equation it should be I/csc(theta), but because i want the cos negative it should be csc(theta) right?

Answer 8

remember they want us to use sin not csc

Answer 9

They want us to write cos(x) in terms of sin(x)

Answer 10

oh shoot thats right

Answer 11

When x is in the 2nd quadrant

Answer 12

Our equation shows us that \[\Huge \cos(\theta)= \sin(\frac{\pi}{2}-\theta)\]

Answer 13

so i just have to manuver that equation into terms of sin

Answer 14

Now \[\Huge \frac{\pi}{2}=90 \] degrees

Answer 15

Now we have to see if we put a negative in front of sin or not

Answer 16

i see how you get that

Answer 17

Ok, well our question asked for the equation of cos in terms of sin. We got that

Now it says that the point of the angle is in the second quadrant, so we might have to play around with the equation like change the pi/2 or put a negative.

What we're going to do is test a point and see if this equation holds true

Now remember the quadrant we're worrying about is the second one so it's all the angles between 90-180 so let's pick a point inbetween those two


We'll use 120 just for random sake. try plugging in cos(120) (make sure your calculator is in deg mode) and tell me what you get

Answer 18

to the first equation you put up right?

Answer 19

Yeah, just put in 120 for \[\Large \theta \]

Answer 20

You can do it to the equation \[\Huge \cos(\theta)= \sin(\frac{\pi}{2}-\theta)\] and see if both sides come out the same, remember that the pi/2 changes to 90

Answer 21

they are the same! -.5

Answer 22

Ok, so we're done (: Good job

Answer 23

thanks for the help!! i really appreciate it!

Answer 24

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