How to Calculate Sin(π/8)^2 - Cos(3π/8)^4 Without a Calculator?

In summary, the task is to find the numerical value of Sin[Pi/8]^2 - Cos[3 (Pi/8)]^4 without using tables or calculators. The approach suggested is to use a standard trigonometric identity to simplify the expression.
  • #1
kenshaw93
10
0

Homework Statement


Without using tables(calculators) find the numerical value of

Sin[Pi/8]^2 - Cos[3 (Pi/8)]^4



Homework Equations






The Attempt at a Solution


I tried changing it to:
1-cos[pi/8]^2 - cos[3pi/8]^4 but have no idea where to go... its really got me scratching my head.

Any ideas? Any help is much appreciated, thank you.
 
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  • #2
Welcome to PF!

Hi kenshaw93! Welcome to PF! :smile:

(have a pi: π and try using the X2 tag just above the Reply box :wink:)

You know what cos and sin of π/4 are …

so use one of the standard trigonometric identities to get to π/8 and 3π/8. :smile:
 

FAQ: How to Calculate Sin(π/8)^2 - Cos(3π/8)^4 Without a Calculator?

What are trigonometric identities?

Trigonometric identities are mathematical equations that relate different trigonometric functions to one another. They are used to simplify and manipulate expressions involving trigonometric functions.

Why are trigonometric identities important?

Trigonometric identities are important because they allow us to solve complex problems involving trigonometric functions, and they also help us establish connections between different trigonometric functions.

How many types of trigonometric identities are there?

There are several types of trigonometric identities, including reciprocal identities, quotient identities, Pythagorean identities, and double angle identities.

How can I remember all these trigonometric identities?

One way to remember trigonometric identities is to understand the patterns and relationships between different trigonometric functions. You can also practice using these identities in various problems to help you remember them better.

Are there any real-life applications of trigonometric identities?

Yes, trigonometric identities have many real-life applications, such as in engineering, physics, astronomy, and navigation. They are also used in fields like computer graphics and signal processing.

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