# Trigonometric identities problem

1. Jul 2, 2010

### angelcase

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values.

I found one of the values using sin^2 (theta) + cos^2 (theta) = 1

I tried using cos (90 + theta)= sin theta to find the second one, but couldn't remember if you were able to distribute the cos...since addition is communitive or whatever that property is called...and get cos 90 + cos theta= sin theta

2. Jul 2, 2010

### JonF

Re: Trig...

I'd use these:

tan(x) = sin(x)/cos(x)
Sin = Opposite / Hypotinuse
.6 = 6/10

3. Jul 2, 2010

### JonF

Re: Trig...

I should talk about this too. You can't distrubte any given function over addition. And cos(90 +x) isn’t sin(x), it’s –sin(x). But in general cos(u + v) = cos(u)cos(v) – sin(u)sin(v)

4. Jul 3, 2010

### angelcase

Re: Trig...

Thank you JonF...the cos(90 + theta)= sin theta was in my text as a trig equation to use...I didn't make it up...I know that the derivative of cos is -sin and the derivative of sin is cos, and tan is sec^2...I get all the derivative stuff..Just seem to have an issue with the basics, which to me is pretty pathetic..On my part.

5. Jul 3, 2010

### Pere Callahan

Re: Trig...

You can if the function in question happens to be linear. The cosine function is apparently not linear so you can not distribute.

6. Jul 3, 2010

### Tedjn

Re: Trig...

To the OP, you should find two possible values from sin2θ + cos2θ = 1. This is because there is both a positive and negative square root.

7. Jul 3, 2010

### Redbelly98

Staff Emeritus
Re: Trig...

Moderator's note: thread moved from General Math to Homework & Coursework Questions area.

8. Jul 4, 2010

### Unit

Re: Trig...

Forget identities! Draw a unit circle with two right triangles in it! The angle at the origin will be θ and the hypotenuse (radius) will be 1. If sinθ = 0.6, where will the 0.6 go? And, given a hypotenuse of 1 and one side, could you find the other side, considering the Pythagorean theorem?

9. Jul 4, 2010

### Redbelly98

Staff Emeritus
Re: Trig...

The OP has already solved half of the problem using the identity
sin^2 (theta) + cos^2 (theta) = 1​
She could either use your graphical method, or she could consider the two solutions for cos(θ) in that equation by taking a negative square root.