Thread: Pre-calc Idenities & math Help me understand this please

Ok I don't understand how to do these 3 types of questions.
Please help me understand how to do them. Thanks for your time.


1. Verify the identity (Can only change one side, and end result must equal each other)
cos^3Xsin^2X=(sin^2X-sin^4X)cosX

2. Sole the equation.
4cosX=1+2cosX

3. Find the exact values of the sine, cosine, and tangent of the angle by using the sum or difference formula.
345 degrees = 300 degrees + 45 degrees

Thanks for any help.

Originally Posted by mrjameslat

Ok I don't understand how to do these 3 types of questions.
Please help me understand how to do them. Thanks for your time.


1. Verify the identity (Can only change one side, and end result must equal each other)
cos^3Xsin^2X=(sin^2X-sin^4X)cosX

left side ... cosx(cos^2x sin^2x) = cosx[(1 - sin^2x)sin^2x] = cosx(sin^2x - sin^4x)

2. Sole the equation.
4cosX=1+2cosX

subtract 2cosx from both sides ...

2cosx = 1

cosx = 1/2 ... x = pi/3, x = 5pi/3

3. Find the exact values of the sine, cosine, and tangent of the angle by using the sum or difference formula.
345 degrees = 300 degrees + 45 degrees

use the sum/difference identities ...

cos(a+b) = cosa cosb - sina sinb

sin(a+b) = sina cosb + cosa sinb

tan(a+b) = (tana + tanb)/(1 - tana tanb)

in addition, you should be very familiar with the values on the unit circle ...

Thanks for the input.
I guess i can make a paradigm of what you said. Thanks a lot.


however with the last one would this be right

345 degrees = 300 degrees + 45 degrees

cos(300+45) = cos(300) cos(45) - sin(300) sin(45)

sin(300+45) = sin(300) cos(45) + cos(300) sin(45)

tan(300+45) = (tan(300) + tan(45))/(1 - tan(300) tan(45))

and would they equal this.
cos=1/2(√2/2)--√3/2(√2/2)=( √2+√6 )/4

sin=-√3/2(1/2)+1/2(√2/2)=(√2-√6)/4

and how would i do the tangent one? thanks again.

Did i do it right?

Originally Posted by mrjameslat

however with the last one would this be right

345 degrees = 300 degrees + 45 degrees

cos(300+45) = cos(300) cos(45) - sin(300) sin(45)

sin(300+45) = sin(300) cos(45) + cos(300) sin(45)

tan(300+45) = (tan(300) + tan(45))/(1 - tan(300) tan(45))

and would they equal this.
cos=1/2(√2/2)--√3/2(√2/2)=( √2+√6 )/4 ... ok

sin=-√3/2(1/2)+1/2(√2/2)=(√2-√6)/4 ... ok

and how would i do the tangent one? tanx = sinx/cosx

... you can also check your results w/ a calculator.

Originally Posted by skeeter

in addition, you should be very familiar with the values on the unit circle ...

I can get all that information by knowing the 45-45-90 triangle, the 30-60-90 triangle, and the graphs of sin and cosine.

Originally Posted by Ackbeet

I can get all that information by knowing the 45-45-90 triangle, the 30-60-90 triangle, and the graphs of sin and cosine.

... and all I need is the 45-45-90 triangle, the 30-60-90 triangle, and the beauty of symmetry.

Out of curiosity, how would you get the values of sin and cosine on the x and y axes via symmetry?

Originally Posted by Ackbeet

Out of curiosity, how would you get the values of sin and cosine on the x and y axes via symmetry?

the picture of the unit circle is color-coded to show that symmetry from quadrant to quadrant.

Yeah, but I'm talking about values that are on the x axis, or on the y axis. By symmetry, how do you know that

I guess I would need to remember the basic definition ... .

Ah, so you'd have to remember something in addition to the 45-45-90, the 30-60-90, and symmetry.

Ok when i try the tan one i get stuck please help?

tan(300+45) = (sina/cosa + sinb/cosb)/(1 – sina/cosa*sinb/cosb) =

( -√3/2/1/2 + √2/2/1/2 )/(1- -√3/2/1/2 * √2/2/1/2)=

(-2√3+2√2) / (1+2√3*2√2)

What do I need to do, or what have I done wrong?
thanks

Originally Posted by mrjameslat

Ok when i try the tan one i get stuck please help?

tan(300+45) = (sina/cosa + sinb/cosb)/(1 – sina/cosa*sinb/cosb) =

( -√3/2/1/2 + √2/2/1/2 )/(1- -√3/2/1/2 * √2/2/1/2)=

(-2√3+2√2) / (1+2√3*2√2)

What do I need to do, or what have I done wrong?
thanks

recheck your values and simplify them before using the sum identity for tangent ...







if you decide to rationalize the denominator, the value will simplify to

"work smart, not hard" thanks a lot!