# Inverse trigonometric function

How to solve without calculator

1. sin(arctan(12/5))

2. cos(arccosx + arcsinx)

Thanks.

You have to know your right triangles.
5 12 13 is one. If the tan is 12/5, then the sin is 5/13. Draw a pic to confirm that.

On the second: Think. Draw any right triangle. Label the angles. Label the hypotenuse as 1, and the one sides as x. The other side will be sqrt (1-x^2). Notice the angle whose sine is x is the complement of the angle whose cosine is x. Does that mean those two angles add to ninety degrees?

can't we do it by taking u=arctan(12/5)

no. arctan(12/5) is not equal to what you started out with.

1. 👍 0
2. 👎 0
3. 👁 278
1. 1.17

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Trigonometry

I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b))

asked by Jen on July 27, 2007
2. ### Pre-Calc

How do I write sin(arcsinx + arccosx) as an algebraic expression?

asked by Anonymous on January 19, 2016
3. ### Math

Arrange these in order from least to greatest: arctan(-sqrt3), arctan 0, arctan(1/2) So far I got the first two values, arctan(-sqrt3), and that's 150 degrees. Arctan 0 would be zero degrees. I'll use just one answer for now, but

asked by Anonymous on August 13, 2009
4. ### Trigonometry

Solve the equation for solutions in the interval 0

asked by Renee on March 7, 2016
5. ### Calculus

Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to

asked by Tracy on October 21, 2006
6. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

asked by hayden on February 23, 2009
7. ### Pre Calclulus

Write the trigonometric expression as an algebraic expression. sin(arcsinx+arccosx)

asked by Anonymous on March 10, 2013
8. ### Trigonometry - Identities

If tan 2x = - 24/7, where 90 degrees < x < 180 degrees, then find the value of sin x+ cos x. I applied various identities and tried manipulating the problem to get sin x + cos x = sin(arctan(-24/7)/2) + cos(arctan(-24/7)/2) I also

asked by Sam on November 14, 2013
9. ### Math-Trig

1. Create an algebraic expression for sin(arccosx-arcsin3x) 2. The cosx=4/5, x lies in quadrant 4. Find sin x/2 3.Determine all solutions in (0,2pie) for sin4xsin^2x=3, cot^2v(3-1)cotx=v(3), cos^2x=cosx, and tan^2x-6tanx+4=0 4.

asked by Hujinson on April 14, 2009
10. ### math

Can anyone help w/ these. 1) Solve the equation in the internal [0deg, 360deg]. a) sin 2x = -sin x b) sin 2T = -1/2 (where T is angle) c) 4 sin^2T = 3 2) Evaluate the expression. sin(arctan 2) 3) Rewrite the following w/o using

asked by chyrl on December 9, 2006

More Similar Questions