 # Precalculus: trigonometry questions and answers

Recent questions in Trigonometry Anthony Kramer 2022-05-24 Answered

### Prove that $\sqrt{3}\mathrm{cos}\left(x\right)+\mathrm{sin}\left(x\right)=2\mathrm{cos}\left(x-\frac{\pi }{6}\right)$ dokezwa17 2022-05-24 Answered

### If $\mathrm{sin}x+{\mathrm{sin}}^{2}x=1$ then find the value of ${\mathrm{cos}}^{8}x+2{\mathrm{cos}}^{6}x+{\mathrm{cos}}^{4}x$ vaganzahi 2022-05-24 Answered

### In $\mathrm{\Delta }ABC$,such $3{\mathrm{sin}}^{2}B+7{\mathrm{sin}}^{2}C=2{\mathrm{sin}}^{2}A+2\mathrm{sin}A\mathrm{sin}B\mathrm{sin}C$, and such $a=|BC|=1$, show that$\mathrm{sin}A=\frac{\sqrt{5}}{5}$I think this problem$3{b}^{2}+7{c}^{2}=2{a}^{2}+2\mathrm{sin}Abc=2+\mathrm{sin}A\cdot bc$where $|AC|=b,|AB|=c$ Kash Brennan 2022-05-24 Answered

### I curious practical solution.(Step by step)$\left(1+\mathrm{tan}{5}^{\circ }\right)\left(1+\mathrm{tan}{10}^{\circ }\right)\left(1+\mathrm{tan}{15}^{\circ }\right)\cdots \left(1+\mathrm{tan}{40}^{\circ }\right)$ Kendrick Pierce 2022-05-24 Answered

### How to derive $\mathrm{sin}\left(2x\right)=\frac{1}{\sqrt{1+{\mathrm{cot}}^{2}\left(2x\right)}}$? raulgallerjv 2022-05-23 Answered

### To find minimum value of $2\mathrm{csc}\left(2x\right)+\mathrm{sec}\left(x\right)+\mathrm{csc}\left(x\right)$ Aditya Erickson 2022-05-23 Answered

### Use the identities$\mathrm{cos}2x=2{\mathrm{cos}}^{2}x-1=1-2{\mathrm{sin}}^{2}x$$\mathrm{sin}x=\mathrm{cos}\left(\frac{\pi }{2}-x\right)$to help evaluate${\int }_{0}^{\pi /2}\sqrt{1-\mathrm{sin}x}\phantom{\rule{thickmathspace}{0ex}}dx$ istupilo8k 2022-05-23 Answered

### Can $\frac{2u\mathrm{sin}\left(\alpha -\beta \right)}{g\mathrm{cos}\beta }=\frac{u\mathrm{cos}\left(\alpha -\beta \right)}{g\mathrm{sin}\beta }$ be reduced to $2\mathrm{tan}\left(\alpha -\beta \right)\mathrm{tan}\beta =1$?The closest I can get is:$\mathrm{tan}\alpha \mathrm{tan}\beta -2{\mathrm{tan}}^{2}\beta =1$Is this correct so far? patzeriap0 2022-05-23 Answered

### Find the exact value of ${\mathrm{sin}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ and the like.a. ${\mathrm{sin}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$b. ${\mathrm{cot}}^{-1}\left(-1\right)$c. ${\mathrm{sec}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$d. ${\mathrm{cos}}^{-1}\left(-\frac{\sqrt{2}}{2}\right)$e. ${\mathrm{tan}}^{-1}\left(-\sqrt{3}\right)$ copafumpv 2022-05-23 Answered

### How does $\int \frac{{\mathrm{cos}}^{4}x}{\sqrt{1-\mathrm{sin}x}}\phantom{\rule{thinmathspace}{0ex}}dx$ simplify to $-\int -{\left(2-u\right)}^{\frac{3}{2}}u\phantom{\rule{thinmathspace}{0ex}}du$ Alaina Marshall 2022-05-23 Answered

### If $a{\mathrm{sin}}^{2}\theta +b{\mathrm{cos}}^{2}\theta =m,a{\mathrm{cos}}^{2}\varphi +b{\mathrm{sin}}^{2}\varphi =n,a\mathrm{tan}\theta =b\mathrm{tan}\varphi$, prove that $\frac{1}{n}+\frac{1}{m}=\frac{1}{a}+\frac{1}{b}$ Richardtb 2022-05-23 Answered

### Given the function:$f:\left[-\frac{\pi }{2},\frac{\pi }{2}\right]\to \mathbb{R}$$f\left(x\right)=\frac{\mathrm{cos}x}{\mathrm{cos}\left(x-a\right)}$ for some $a\in \mathbb{R}$Is it possible to convert it to some kind of translated / otherwise transformed tanx or cotx? vamosacaminarzi 2022-05-23 Answered

### $\mathrm{tanh}\left(x+y\right)=\mathrm{tanh}\left(z\right)\to x+y=z?$?Why is this true? hawwend8u 2022-05-23 Answered

### How would you find the exact roots of $y={x}^{3}+{x}^{2}-2x-1$? meindwrhc 2022-05-23 Answered

### Prove that $\frac{1}{2}\sqrt{4{\mathrm{sin}}^{2}\left({36}^{\circ }\right)-1}=\mathrm{cos}\left({72}^{\circ }\right)$ Emery Boone 2022-05-23 Answered

### Unfortunately I have not found anything about the rules for this. Is there a way to simplify this? $\frac{\mathrm{Arctan}\left(\frac{a}{2}\right)}{\mathrm{Arctan}\left(\frac{b}{2}\right)}$ Yasmin Camacho 2022-05-23 Answered

### Given that $\mathrm{tan}u=0.4$ & $\pi .Finding the value of $\mathrm{tan}\frac{u}{2}$ wanaopatays 2022-05-22 Answered

### How to solve ${\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x-1=0$ ? skottyrottenmf 2022-05-22 Answered

### How does $\mathrm{cos}\left(x\right)\cdot \mathrm{cos}\left(\frac{3}{2}x\right)$ become $\frac{1}{2}\left(\mathrm{cos}\left(\frac{1}{2}x\right)+\mathrm{cos}\left(\frac{5}{2}x\right)\right)$? Elisha Kelly 2022-05-22 Answered

### Find the period of $\mathrm{cos}x-\mathrm{sin}x$Show that f had period of $2\pi$How do you find the period of a function that has several trigonometric functions like this one?I tried converting them all to sine:$f\left(x\right)=\sqrt{1-{\mathrm{sin}}^{2}x}-\mathrm{sin}x$But what do I do next?

The majority of Trigonometry Math problems are quite easy to solve when you have the list of answers that help you see the logic and reasoning. Looking at various examples will help you to see how certain questions are related to provided solutions.