Introduction to Trigonometry Practice 2: Standard Values and Relationships

Section A: Standard and Boundary Angles

Question 1mcq

What is the exact value of

\sin 30^\circ

?

A.

\frac{1}{\sqrt{2}}

B.

1

C.

\frac{1}{2}

D.

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

Question 2mcq

Which pair of values is correct?

A.

\tan 60^\circ=1

and

\cos 45^\circ=\frac{1}{2}

B.

\cos 60^\circ=\frac{1}{2}

and

\tan 45^\circ=1

C.

\sin 60^\circ=\frac{1}{2}

and

\tan 45^\circ=0

D.

\cos 30^\circ=\frac{1}{2}

and

\sin 45^\circ=1

Question 3mcq

Which value is defined and correct?

A.

\cos 0^\circ=1

B.

\tan 90^\circ=0

C.

\sec 90^\circ=1

D.

\cosec 0^\circ=1

Question 4mcq

Evaluate

2\sin 30^\circ+\cos 60^\circ

.

A.

1

B.

2

C.

\frac{1}{2}

D.

\frac{3}{2}

Question 5mcq

Evaluate

\tan^2 45^\circ+\cos^2 60^\circ

.

A.

1

B.

\frac{1}{4}

C.

\frac{5}{4}

D.

\frac{3}{4}

Section B: Relationships

Question 6mcq

If

A=35^\circ

, then

\sin(90^\circ-A)

equals:

A.

\sec 35^\circ

B.

\cos 35^\circ

C.

\sin 35^\circ

D.

\tan 35^\circ

Question 7mcq

Which identity is correct for acute angle

A

?

A.

\cot(90^\circ-A)=\tan A

B.

\sin(90^\circ-A)=\sin A

C.

\sec(90^\circ-A)=\sec A

D.

\tan(90^\circ-A)=\tan A

Question 8mcq

If

\sec A=\frac{5}{3}

, what is

\cos A

?

A.

\frac{5}{3}

B.

\frac{4}{5}

C.

\frac{5}{4}

D.

\frac{3}{5}

Question 9mcq

Which reciprocal relationship is correct?

A.

\cosec A=\frac{1}{\cos A}

B.

\tan A=\frac{1}{\sin A}

C.

\cot A=\frac{1}{\tan A}

D.

\sec A=\frac{1}{\sin A}

Question 10mcq

A student writes

\tan 90^\circ=\frac{\sin 90^\circ}{\cos 90^\circ}=\frac{1}{0}

and calls it

0

. What should be concluded?

A.

\tan 90^\circ=-1

B.

\tan 90^\circ

is not defined.

C.

\tan 90^\circ=0

D.

\tan 90^\circ=1