Choose the one alternative that best completes the statement

Choose the one alternative that best completes the statement or answers the question. Find the exact value. Given that tan theta = 7/24 with 0 in quadrant III, find sin 2theta. 527/625 -336/625 336/625 -527/625 solve. Round to the nearest ten-thousandth when necessary. Given that sin theta = 0.8352 and that theta is in quadrant I, find sin(theta/2). -0.9013 0.4744 0.5218 0.4269 SHORT ANSWER. Write the word or phase that best completes each statement or answers the question.Prove the identity. 1 - tanx/1 + tanx = 1 - sin2x/cos2x csx - secx/cscx + secx = cos 2x/1 + sin2x sin(u -v)/sinu cosv = secu cosv - csc u sin v Choose the one alternative that best completes the statement or answers the question. Evaluate tan(cos^-1 squareroot3/2) 1/2 squareroot2/2 squareroot3/3 squareroot 3. Write the word or phrase that best completes each statement or answers the question. cos^-1(tan(-3 pi/4)) Find. tan(cos^-1 x)

Solution

I will answer 11th and 13th post other questions separately

let us say theta =\'x\'

tanx= 7/24 x is in 1st quadrant

sec^2x -tan^2x =1

sec^2x = 1 + (7/24)^2

sec^2x = 1 +49/576

sec^2x = 625/576

secx = 25/24 (since x is in 1st quadrant)

cosx = 1/secx = 24/25

sin^2x +cos^2x =1

sin^2x = 1-cos^2x

sin^2x = 1 - (24/25)^2

sin^2x = 1-576/625

sin^2x = 49/625

sinx = 7/25

sin2x = 2sinx.cosx

sin2x = 2.(7/25) . (24/25)

sin2x = 336/625

option C) is correct answer

13).

sinx =0.8352

x = arc sin(0.8352)

x = 56.6 degree approximately

sin(x/2) = sin(56.6/2) = 0.47436 =0.4744

option B)