How do you find the exact value in radians without using a calculator ${cos}^{- 1} (\frac{1}{2})$ $cos^-1 (1/2)$ ?

Question

How do you find the exact value in radians without using a calculator ${cos}^{- 1} (\frac{1}{2})$ $cos^-1 (1/2)$ ?

1 Answer

Impact of this question

9598 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-06T06:27:11

${cos}^{- 1} (\frac{1}{2}) = {(\frac{π}{3})}^{R}$ $cos^-1(1/2)=(pi/3)^R$

Explanation:

We know that ,

$(1) {cos}^{- 1} (cos θ) = θ, w h e r e, θ \in [0, π]$ $color(red)((1)cos^-1(costheta)=theta ,where, theta in [0,pi]$

$(2) cos (\frac{π}{3}) = \frac{1}{2}$ $(2)cos(pi/3)=1/2$

Using $(2)$ $(2)$ ,we get

${cos}^{- 1} (\frac{1}{2}) = {cos}^{- 1} (cos (\frac{π}{3}))$ $cos^-1(1/2)=color(red)(cos^-1(cos(pi/3))$ $and \frac{π}{3} \in [0, π]$ $and color(red)(pi/3 in[0,pi]$

$cos^-1(1/2)=color(red)(pi/3).....to[color(red)(apply (1))]$

Hence , $cos^-1(1/2)=pi/3$ $radians$

Science

Math

Humanities

... and beyond

How do you find the exact value in radians without using a calculator ${cos}^{- 1} (\frac{1}{2})$ $cos^-1 (1/2)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the exact value in radians without using a calculator cos^-1 (1/2)cos−1(12)cos^-1 (1/2)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the exact value in radians without using a calculator ${cos}^{- 1} (\frac{1}{2})$ $cos^-1 (1/2)$ ?