Processing math: 50%

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Exact Value of cos 22½°

How to find the exact value of cos 22½° using the value of cos 45°?

Solution:

22½° lies in the first quadrant.

Therefore, sin 22½° is positive.

For all values of the angle A we know that, cos A = 2 cos2 A2  - 1

⇒ 1 + cos A = 2 cos2 A2

⇒ 2 cos2 A2 = 1 + cos A

⇒ 2 cos2 22½˚ = 1 + cos 45°

⇒ cos2 22½˚ = \frac{1 + cos 45°}{2}

⇒ sin^{2} 22½˚ = \frac{1 + \frac{1}{\sqrt{2}}}{2}, [Since we know cos 45° = \frac{1}{√2}]

⇒ cos 22½˚ = \sqrt{\frac{1}{2}(1 +  \frac{1}{\sqrt{2}})}, [Since, cos 22½˚ > 0]

⇒ cos 22½˚ = \sqrt{\frac{\sqrt{2} + 1}{2\sqrt{2}}}

⇒ cos 22½˚ = \frac{1}{2}\sqrt{2 + \sqrt{2}}

Therefore, cos 22½˚ = \frac{1}{2}\sqrt{2 + \sqrt{2}}

● Submultiple Angles








11 and 12 Grade Math

From Exact Value of cos 22 and Half Degree to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

RSS

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 19, 25 02:53 PM

    Worksheet on Average
    In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems.

    Read More

  2. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More