Trigonometric Functions I - Challenging

Question 1: Find the coordinates of the point on the circle which was obtained by rotating of point

P (1; 0)

by the angle of

- 90 °

.

A

P 1 (- 1; 0)

B

P 1 (0; 1)

C

P 1 (0; - 1)

D

P 1 (0; 0)

Question 2: Solve the expression

2 {sin}^{2} \frac{π}{4} + {cos}^{2} \frac{π}{6}

.

A

0

B

1.5

C

1

D

1 \frac{3}{4}

Question 3: Simplify the expression:

\sin α - |\sin α|

, if

α

is located in the third coordinate quarter.

A

1

B

2 s i n α

C

s i n α

D

0

Question 4: Compare two expressions

\sin 60 °

and

\sin \frac{7 π}{6}

.

A

\sin 60 ° = \sin \frac{7 π}{6}

B

\sin 60 ° \geq \sin \frac{7 π}{6}

C

\sin 60 ° > \sin \frac{7 π}{6}

D

\sin 60 ° < \sin \frac{7 π}{6}

Question 5: Find the period (

T

) of the function

y = t g \frac{6 x}{7}

.

A

2 π

B

π

C

\frac{6 π}{7}

D

\frac{7 π}{6}

Question 6: Is the equation

c o s α = 2 c o s 59 °

possible?

A

No, it’s not

B

Yes, it is

C

Yes, it is, only if

α > 0

D

No, it’s not, unless

α < 0

Question 7: Is the equation

c o s α = t g \frac{π}{10}

possible?

A

Yes, it is

B

No, it’s not

C

No, unless

α є [180 °; 270 °]

D

Yes, only if

α є [90 °; 180 °]

Question 8: Find the answer of the expression

\frac{5 c o s α + 6 s i n α}{2 s i n α - 5 c o s α}

, if

t g α = \frac{1}{2}

.

A

- 2

B

- 2 s i n α

C

- 2 c o s α

D

- 1

Question 9: Simplify the expression

t g 10 ° + t g 50 ° + \sqrt{3} t g 10 ° t g 50 °

.

A

\sqrt{3}

B

t g 50 °

C

t g 10 °

D

- \sqrt{3}

Question 10: Simplify the expression

\frac{t g (π - x) s i n (\frac{3 π}{2} + x)}{\cos (π + x) c t g (\frac{3 π}{2} + x)}

.

A

- 1

B

t g x

C

- c t g x

D

1

Test: Trigonometric Functions I - Challenging

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