1. ## Two trig question with squares and radians

Ok, I know the Pythagorean identities but can't seem to solve these two question.

Evaluate. Give exact anwser.
sin² π/6 - tan² π/4 + cos² π/6

so all I can do on this question so far is use the identity sin x + cos x= 1 to get to

1 - tan² π/4

then I am lost.

The next question I have no idea what to do.

Solve the following equation

1 - 2 cos²Θ = -sinΘ, 0<Θ<2π

2. Originally Posted by Apathy
Ok, I know the Pythagorean identities but can't seem to solve these two question.

Evaluate. Give exact anwser.
sin² π/6 - tan² π/4 + cos² π/6

so all I can do on this question so far is use the identity sin x + cos x= 1 to get to

1 - tan² π/4

then I am lost.
Hint: $\displaystyle \tan\left(\frac{\pi}{4}\right) = 1$

3. Originally Posted by Apathy
The next question I have no idea what to do.

Solve the following equation

1 - 2 cos²Θ = -sinΘ, 0<Θ<2π
This is the same as

$\displaystyle -(1-2\sin^2\theta)= -\sin\theta$

Make $\displaystyle \sin\theta = a$ and solve as a quadratic.

4. Originally Posted by pickslides
Hint: $\displaystyle \tan\left(\frac{\pi}{4}\right) = 1$
Does that mean that tan π/4² will give me +1 because (-1)²=1?
Will my awnser be 2?
thank you!

5. Originally Posted by pickslides
This is the same as

$\displaystyle -(1-2\sin^2\theta)= -\sin\theta$

Make $\displaystyle \sin\theta = a$ and solve as a quadratic.
Whoa! What identity was that? cos magically became sin!?

i got to the point sinΘ=1/2 or sinΘ=-1. Now do I reject -1 because because 0<Θ<2π or am I missing something? Also, how do I get rid of the sin?

I realize this stuff is elementary but I feel that my teacher gave an insufficient explanation for the trig unit.

6. Originally Posted by Apathy
Does that mean that tan π/4² will give me +1 because (-1)²=1?
Will my awnser be 2?
thank you!
It's 1 not -1. (1)^2 = 1. And so you have 1 - 1 = 0, not 2. You need to take more care with basic arithmetic.

Originally Posted by Apathy
Whoa! What identity was that cos magically became sin!?
The left hand side of the equation you posted has been converted into $\displaystyle -1 + 2 \sin^2 \theta$ using the Pythagorean Identity. Now you're are expected to re-arrange the resulting equation into a quadratic equation. Look in your class notes or textbook for a similar example.

7. Originally Posted by mr fantastic
It's 1 not -1. (1)^2 = 1. And so you have 1 - 1 = 0, not 2. You need to take more care with basic arithmetic.

The left hand side of the equation you posted has been converted into $\displaystyle -1 + 2 \sin^2 \theta$ using the Pythagorean Identity. Now you're are expected to re-arrange the resulting equation into a quadratic equation. Look in your class notes or textbook for a similar example.

Thank you. I was under the impression 1-tan² π/4 meant that when I used the identity that the I would include the negative sign but then I realized that the negative is not part of the identity so your way does make perfect sense. (sorry for that rant, I am not even sure that was coherent).

Here is all my work for the second question. Still can't find the answer... maybe math isn't my forte

8. Originally Posted by Apathy

Here is all my work for the second question. Still can't find the answer... maybe math isn't my forte

$\displaystyle \sin(\theta)= \frac{1}{2}\implies \theta =\frac{\pi}{6}$

$\displaystyle \sin(\theta)= -1\implies \theta =\frac{3\pi}{2}$