Test: Trigonometric Functions I - Challenging

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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° .
P1 0;0
P1 0;1
P1 0;1
P1 1;0
Question 2:   Solve the expression 2 sin 2 π 4 + cos 2 π 6 .
1
1 3 4
0
1.5
Question 3:   Simplify the expression:   sinα sinα ,  if   α   is located in the third coordinate quarter.
sinα
2sinα
 0
1
Question 4:   Compare two expressions sin60° and sin 7π 6 .
sin60° < sin 7π 6
sin60°= sin 7π 6
sin60°  sin 7π 6
sin60° > sin 7π 6
Question 5:   Find the period ( T ) of the function y=tg 6x 7 .
6π 7
2π
π
7π 6
Question 6:   Is the equation cosα=2cos59° possible?
No, it’s not
Yes, it is, only if α>0
No, it’s not, unless α<0
Yes, it is
Question 7:   Is the equation cosα= tg π 10 possible?
Yes, it is
No, unless α є  180°;270°
Yes, only if α є  90°;180°
No, it’s not
Question 8:   Find the answer of the expression 5cosα+6sinα 2sinα5cosα , if tgα= 1 2 .
 2
 2sinα
2cosα
 1
Question 9:   Simplify the expression tg10°+tg50°+ 3 tg10°tg50° .
tg10°
3
3
tg50°
Question 10:   Simplify the expression tg πx  sin 3π 2 +x cos π+x ctg 3π 2 +x .
1
ctgx
tgx
1