Quiz about Trigonometry 1

Question 1

Is tanA the reciprocal of cotA

Accepted Answer

YES

Answer

NO

Question 2

If $$\Delta ABC$$ is right angled at C, then find the value of cos (A+B)

Accepted Answer

0

Answer

1

Answer

$$\frac{1}{2}$$

Answer

$$\frac{\sqrt{3}}{2}$$

Question 3

Which function is the reciprocal function of the cosine?

Accepted Answer

secant

Answer

sine

Answer

cosecant

Answer

tangent

Question 4

What is the exact value $$\cot\left(\frac{10\pi}{3}\right)$$ ?

Accepted Answer

$$\frac{\sqrt{3}}{3}$$

Answer

$$\frac{\sqrt{3}}{2}$$

Answer

$$-\sqrt{3}$$

Answer

$$\frac{1}{3}$$

Question 5

What is the exact value of $$\sin\left(\frac{7\pi}{6}\right)$$ ?

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$\frac{1}{2}$$

Answer

$$-\frac{\sqrt{3}}{2}$$

Answer

$$\frac{\sqrt{3}}{2}$$

Question 6

Solve the equation $$\cos x+\frac{1}{2}=0$$ for $$0\le x\le2\pi\pi$$ .

Accepted Answer

$$x=\frac{2\pi}{3},\ \frac{4\pi}{3}$$

Answer

$$x=\pi,\frac{5\pi}{3}$$

Answer

$$x=\frac{\pi}{3},\ 2\pi$$

Answer

$$x=\frac{\pi}{3},\ \frac{5\pi}{3}$$

Question 7

Solve the equation $$\sin\left(x+\frac{\pi}{3}\right)=1$$ for $$0\le x\le4\pi$$ .

Accepted Answer

$$x=\frac{\pi}{6},\ \frac{13\pi}{6}$$

Answer

$$x=\frac{11\pi}{6},\frac{23\pi}{6}$$

Answer

$$x=\frac{\pi}{6},\ 2\pi$$

Answer

$$x=\frac{2\pi}{3},\ \frac{7\pi}{6}$$

Question 8

Solve the equation $$2 an^2x-6=0$$ for $$0\le x\le2\pi\pi$$ .

Accepted Answer

$$x=\frac{\pi}{3},\ \frac{2\pi}{3},\ \frac{4\pi}{3},\ \frac{5\pi}{3}$$

Answer

$$x=\frac{2\pi}{3},\ \pi,\frac{4\pi}{3},\ \frac{5\pi}{3}$$

Answer

$$x=\frac{\pi}{3},\ \pi,\frac{4\pi}{3},\ 2\pi$$

Answer

$$x=\frac{2\pi}{3},\ \pi,\ \frac{4\pi}{3},\ \frac{5\pi}{3}$$

Question 9

Solve $$\cos x+\sin x=0$$

Accepted Answer

$$x=\frac{3\pi}{4},\ \frac{7\pi}{4}$$

Answer

$$x=\frac{\pi}{2},\ \frac{7\pi}{4}$$

Answer

$$x=\pi,\ \frac{3\pi}{2}$$

Answer

$$x=\frac{3\pi}{4},\ \frac{5\pi}{4}$$

Question 10

Solve $$ an\left(x-\frac{\pi}{4} ight)-\sqrt[]{3}=0$$ for $$0\le x\le2\pi$$ .

Accepted Answer

$$x=\frac{7\pi}{12},\ \frac{19\pi}{12}$$

Answer

$$x=\frac{11\pi}{6},\frac{23\pi}{12}$$

Answer

$$x=\frac{\pi}{6},\ 2\pi$$

Answer

$$x=\frac{\pi}{3},\frac{\pi}{2}$$

Question 11

Solve $$8\sin\left(x+\frac{\pi}{6}\right)+4=0$$ for $$-2\pi\le x\le2\pi$$ .

Accepted Answer

$$x=-\pi,\ \frac{-\pi}{3},\ \pi,\ \frac{5\pi}{3}$$

Answer

$$x=-2\pi,\ -\pi,\ \pi,\ \frac{5\pi}{3}$$

Answer

$$x=\frac{-4\pi}{3},\ 0,\ \frac{2\pi}{3},\ \frac{4\pi}{3}$$

Answer

$$x=\ \frac{-5\pi}{3},\frac{-2\pi}{3},\frac{-\pi}{3},\ \frac{\pi}{3}$$

Question 12

Solve $$4 an y=\cot y$$ for $$0\le y\le2\pi$$ . Answers given to 3sf.

Accepted Answer

0.464

Accepted Answer

2.68

Accepted Answer

3.61

Accepted Answer

5.82

Answer

-0.464

Question 13

Solve $$\sin3x=-1$$ for $$0\le x\le2\pi$$ .

Accepted Answer

$$\frac{\pi}{2}$$

Accepted Answer

$$\frac{5\pi}{6}$$

Accepted Answer

$$\frac{7\pi}{6}$$

Answer

$$\frac{\pi}{6}$$

Question 14

Solve $$ an\left(x+\frac{\pi}{9} ight)=0.8$$ for $$0\le x\le2\pi$$ . Answers given to 3sf.

Accepted Answer

0.326

Accepted Answer

3.47

Answer

2.12

Answer

5.26

Question 15

Solve $$2 an^2y+5\sec y+1=0$$ for $$0\le y\le2\pi$$ .

Accepted Answer

$$\frac{2\pi}{3}$$

Accepted Answer

$$\frac{4\pi}{3}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{5\pi}{3}$$

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