trigonometry
posted by kiko .
given that sin alpha/2 = 2/3, and that alpha/2 is in quadrant II, determine the exact values of all trig functions for alpha.

let alpha/2 = A/2
sin A/2 = 2/3
then cos A/2 = √5/3
sin A = 2(sin A/2)(cos A/2) = 2(2/3)(√5/3) = 4√5/9
make a sketch,
opposite = 4√5, hypotenuse = 9
adj^2 + 80 = 81
adj = 1
sin alpha = 4√5/9
cos alpha= 1/9
tan alpha = 4√5
I am sure you can find the three reciprocal values
Respond to this Question
Similar Questions

trig
express 20sin theta + 4 cos theta as R sin(theta + alpha) R sin(theta + alpha) = R cos(alpha)sin(theta) + R sin(alpha)cos(theta) > Rcos(alpha) = 20 Rsin(alpha) = 4 The xy coordinates of a point on a circle of radius R that … 
trig
Please find sin (alpha/2) and cos (alpha/2) sec alpha = 3, pi/2 < alpha < 0 
trig
The terminal side of angle alpha is in the fourth quadrant, and sin alpha=1/2, find the values of the other functions. 
Trigonometry/ Please Help
Given sine of alpha=2/3 and cosine of alpha is less than zero, find the exact value of the other five trigonometric functions. 
trig
FInd the exact value pf the 6 trig function of alpha Given: point (2,6) on the terminal side of the angle in standard position sin alpha cos alpha tan alpha sec alpha csc alpha cot alpha 
precal
when solving for all solutions how do I work out this problem: cos4(alpha)=cos2(alpha) and when verifying each identity how do I complete this problem: sin (alpha/2)=sec alpha 1/2sin (alpha/2)sec alpha 
trig
evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(betaalpha) … 
Math
sec(alpha) = 4(√(5))/5 find exact values at alpha for the remaining five trig functions 
Trigonometry
Given that sin alpha = 15/17 and 360 <alpha<360 find all values of alpha to two decimal places. Help Please! 
algebra
if sin alpha is 0.28° where 0° is less than or equal to alpha less than or equal to 90°, evaluate cos alpha, tan alpha, sec alpha, cosec alpha and cot alpha. please help, it's urgent.