Example of Double Angle Formulas

Precalculus: Compute the sine and cosine of theta = 2 tan^{-1}(-3/4). We first compute the sine and cosine for tan^{-1}(-3/4). Then we apply the double angle formulas for sine and cosine.

Category:

Education

Tags:

• Mathematics
• precalculus
• inverse
• tangent
• double
• angle
• formula
• cosine
• sine
• right
• triangle
• trig
• CAST
• method

[oxygenlifeless]

..u ddnt use half angle in that problem?double angle i mean.... u just find the hypotenuse of tan 3/4....... then u use Pythagorean theorem. then u just put answer it cos teta= 4/5 and sine teta is -3/5.. wheres the double angle formula in their? im just confuse but don't mean my question.. its just nothing.. . but if u can tell me.. plss reply at this comment thanks

[MathDoctorBob]

@oxygenlifeless Thanks for the question. There are two parts to this problem:

For Step 1, we save the factor of 2 in theta until Step 2. Here we want to fins sine and cosine of theta' = tan^{-1}(-3/4). Note: you could just call theta' = theta/2, but then you have to carry that 2 around the calculations.

The double angle formulas are given in the lines with cos(2O') and sin(2O') in Step 2. theta = 2theta'.

Let me know if that helps. - Bob

[oxygenlifeless]

@MathDoctorBob oh so in the first place u use tan in the second step you use cos and sine.. now i understand and thanks for this im from philippines taking up electrical engineering kinda creepy subject was the spherical trigonometry thanks for this..it helps soo much,, and sorry for my english i ddnt master my english since highschool kinda hard to use english :(

[MathDoctorBob]

@oxygenlifeless Glad to be of help! No worries about the English; I have no problem understanding you. Good luck with EE! - Bob

[oxygenlifeless]

@MathDoctorBob thank you sir...your a great professor

[oxygenlifeless]

..u ddnt use half angle in that problem? u just find the hypotenuse of tan 3/4....... then u use Pythagorean theorem. then u just put answer it cos teta= 4/5 and sine teta is -3/5.. wheres the half angle formula in their? im just confuse but don't mean my question.. its just nothing.. . but if u can tell me.. plss reply at this comment thanks