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Trigonometric Questions Dealing with Identities PART I

Updated on May 8, 2009

Trigonometric Questions

The following are questions that you may see using your trig identities.

If you do not remember your Trig identities, go to this website:

http://www.sosmath.com/trig/Trig5/trig5/trig5.html 

Please visit:

www.prepteststore.com for more math and test tips.  I am creating more hubs dedicated to math topics, so please check periodically for new hubs.

EXAMPLE 1.a

What is the value of 1-sin2(2x) if cos2(x)=1 in the domain [0,π]?


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a.  1-sin2(2x)=cos2(2x)

You could use the half angle formula, but cos2(x)=1 when x=0 and that is the only time.  If you double the angle 0, then it will still be zero, so the answer is 1.

Example 1.b

Without the use of a calculator, find the value of -(sinx+cosx)(sinx-cosx) given that x=15 degrees.

a. Expand and you get -(sin2x-cos2x)=-sin2x+cos2x=cos(2x)=cos(2(15))=cos(30)= square root of three divided by 2 

sqrt(3)/2

Example 2.a

Note: √ represents square root 

Given √(1-sin2x)(2/√(1+cot2x)), what is the value of this expression when x=15 degrees (no calculator allowed).

square root of all(1-sin2x) and square root of all (1+cot2x) 

a. (1-sin2x)=cos2x, square root of this is simply cosx 

b. (1+cot2x)=cscx, 2/cscx=2sinx because cscx=1/sinx and 1/(1/sinx)=sinx

Now the product is 2sinxcosx=sin2x=sin(2(15))=sin30=1/2 


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