Inverse trigonometric function

posted by .

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.

  • Inverse trigonometric function -

    1.17

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math trigg.

    which triangles do you use COS SIN or TAN?
  2. 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 …
  3. 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 trigonometric …
  4. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
  5. 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)) sin(a-b)=sinacosb-cosasinb …
  6. math

    Eliminate the parameter (What does that mean?
  7. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
  8. MathsSs triG

    Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-360)sin(90-x)tan(-x)/cos(90+x) to a single trigonometric ratio B.hence or otherwise without using a calculator,solve for X if 0<X<360. sin(x-360)sin(90-x)tan(-x)/cos(90+x) …
  9. calculus trigonometric substitution

    ∫ dx/ (x^2+9)^2 dx set x = 3tan u dx = 3 sec^2 u du I = 3 sec^2 u du / ( 9 tan^2 u + 9)^2 = 3 sec^2 u du / ( 81 ( tan^2 u + 1)^2 = sec^2 u du / ( 27 ( sec^2 u )^2 = du / ( 27 sec^2 u = 2 cos^2 u du / 54 = ( 1 + cos 2u) du / 54 …
  10. Trigonometry

    Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 …

More Similar Questions