If cosine theta equals one over six, what are the values of sin θ and tan θ?
a) sine theta equals plus or minus seven times square root of five over six, tangent theta equals plus or minus seven times square root of five
b) sine theta equals plus or minus square root of thirty-five over six, tangent theta equals negative seven times square root of five
c) sine theta equals plus or minus seven times square root of five over six, tangent theta equals negative square root of thirty five
d) sine theta equals plus or minus square root of thirty-five over six, tangent theta equals plus or minus square root of thirty five

Option D.  sine theta equals plus or minus square root of thirty-five over six, tangent theta equals plus or minus square root of thirty five

Step-by-step explanation:

we have that

If the cosine is positive, then the angle theta lie on the first or fourth Quadrant

therefore

The sine of angle theta could be positive (I Quadrant) or negative (IV Quadrant) and the tangent of angle theta could be positive (I Quadrant) or negative (IV Quadrant)

step 1

Find

Remember that

we have

substitute

so

sine theta equals plus or minus square root of thirty-five over six

step 2

Find

Remember that

we have

substitute

tangent theta equals plus or minus square root of thirty five

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°