Mathematics: For what values of θ is sinθ cosθ when 0 ≤ θ π ?Will mark brainliest and 50 points for first to answer!

For what values of θ is sinθ cosθ when 0 ≤ θ π

Ответ:

batmanmarie2004

27.01.2022

Mathematics

$0 \le \theta < \frac{\pi}{4}$

=========================================================

How to get this

Use the unit circle to note that $\sin\theta = \cos\theta = \frac{\sqrt{2}}{2}$ when $\theta = \frac{\pi}{4}$ (aka 45 degrees)

Beyond this point, cosine is smaller than sine. This means that anything from 0 to pi/4 will have sine be smaller than cosine. It might help to graph y = sin(x) and y = cos(x) on the interval from x = 0 to x = pi.

The two curves y = sin(x) and y = cos(x) intersect at the point $\left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right)$

-------------------------------

Here's a more detailed picture of whats going on.

$\sin \theta < \cos \theta\\\\\sin \theta < \sqrt{1-\sin^2\theta}\\\\\sin^2 \theta < 1-\sin^2\theta \\\\2\sin^2 \theta < 1\\\\\sin^2 \theta < \frac{1}{2}\\\\\sin \theta < \sqrt{\frac{1}{2}}\\\\\sin \theta < \frac{1}{\sqrt{2}}\\\\\sin \theta < \frac{\sqrt{2}}{2}\\\\\theta < \arcsin\left(\frac{\sqrt{2}}{2}\right)\\\\\theta < \frac{\pi}{4}\\\\$

Intersect the intervals $0 \le \theta < \pi$ and $\theta < \frac{\pi}{4}$ and you'll end up with the final answer $0 \le \theta < \frac{\pi}{4}$

0,0(0 оценок)

Ответ:

diegomacias2411

01.12.2020

Mathematics

x < -6

Step-by-step explanation:

-2x - 4 > 8

-2x > 12

x < -6, you have to flip the inequality when you multiply or divide by a negative

0,0(0 оценок)

For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?
Will mark brainliest and 50 points for first to answer!

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?Will mark brainliest and 50 points for first to answer!

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?
Will mark brainliest and 50 points for first to answer!