Question

Alg & Trig (Question in replies)

Answer 1

What are the solutions? (Interval of 0-2pi)
\[\cos(2 \theta-\pi/2)=1\]

Answer 2

I know that cos(0rad)=1, but what's next?

Answer 3

one second

Answer 4

Take all the time you need.

Answer 5

ok back ..

Are you familiar with the angle addition property?
sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

Answer 6

Not well, no.

Answer 7

you can figure it using the arccosine like the last one ...

\[\cos(2\theta -\pi/2)=1\]
\[2\theta-\pi/2=\cos^{-1} (1)\]
\[2\theta-\pi/2=0\]

Answer 8

Ok, that's simple enough. That works down to theta = pi/4. MML confirms that's correct, but that there's a second solution.

Answer 9

oh right..

Answer 10

If you look at the equation , it asks, The cosine of what angle is 1?

On the interval 0 to 2pi, the x coordinate on the unit circle is 1 when the angle is 0 or 2pi.

Answer 11

Ah, so we can substitute 2pi in place of 0 as well.

Answer 12

5pi/4 or pi/4.

Answer 13

The solution for
\[\cos(\theta)=1\]
is
\[\theta=\cos^{-1} (1)=2\pi*n\]
for n=1,2,3...

Answer 14

We can continue with the next one here should you have time. https://gyazo.com/c976c82b5d703bc85e4cb6db0ac8e9f5

Answer 15

right, there are two angles to use, 0 and 2pi

Answer 16

I'm confused right at the start here. Tangent lacks an angle at -1, so would it be undefined?

Answer 17

Remember what the tan(x) graph looks like... See how the values can be any real number?