SOLUTION: sin theta = cos (theta - 30°) theta is +ve acute angle. Find sin theta + cos theta.

Algebra.Com
Question 473053: sin theta = cos (theta - 30°) theta is +ve acute angle. Find sin theta + cos theta.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

sinq = cos(q - 30°)

The word "cosine" is an abbreviation for "complement's sine"

If the sine of one positive acute angle equals the
cosine of another positive acute angle, then the
angles are complementary.  Therefore:

q + (q - 30°) = 90°

  q + q - 30° = 90°
    
     2q - 30° = 90°
 
           2q = 120°

            q = 60°  

sinq = 

cosq = 

sinq + cosq = .

Edwin
RELATED QUESTIONS

If theta is an acute angle and sin theta =cos theta, find 2Tan square theta + sin square... (answered by lwsshak3)
solve cos theta = sin theta ( theta + 30 ) (answered by ikleyn)
if theta is an acute angle and cos theta = 1/2, find sin theta and tan... (answered by lwsshak3)
sin theta + cos theta = cos 2... (answered by fractalier)
For what radian measure of acute angle theta is sin theta= cos... (answered by ikleyn)
Which expression is equivalent to sin(theta - 2pi)? -cos(theta) cos(theta) -sin(theta) (answered by Boreal,macston)
simplify sin theta/cos theta tan... (answered by josgarithmetic)
If sin theta=3/4 and theta is an acute angle, what is the value of (tan theta)(cos... (answered by stanbon)
What is an acute angle theta that satidfies the equation sin theta= cos(2 theta + 33... (answered by lwsshak3)