Question

Sin(60)= V3/2, cos(60)=1/2Trig: use the given function values and the trigonometric identities to find the exact value of each indicated trigonometric function a. Sin(30)b. Cos(30)c. Cot(60)

Answer 1

we know that

Sine or Cosine of a Half Angle is giving by the formulas

$\sin (\frac{x}{2})=+-\sqrt{\frac{(1-\cos x)}{2}}$$\cos (\frac{x}{2})=+-\sqrt{\frac{(1+\cos x)}{2}}$

step 1

Find the value of Sin(30)

so

$\sin (\frac{60}{2})=+-\sqrt{\frac{(1-\cos 60)}{2}}$

substitute the given values

cos(60)=1/2

$\sin (30)=+-\sqrt{\frac{(1-1/2)}{2}}=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}$

step 2

Find the value of Cos(30)

substitute the given values in the formula above

$\cos (\frac{60}{2})=+-\sqrt{\frac{(1+\cos 60}{2}}$$\cos (30)=+-\sqrt{\frac{(1+1/2)}{2}}=\sqrt{\frac{3}{4}}=V3/2$

step 3

Find the value of Cot(60)

REmember that

Cot=cos/sin

so

substitute

cot(60)=cos(60)/sin(60)

cot(60)=(1/2)/(V3/2)=V3/3