Help me my teachers pleasevery importient 1what is Expresse

Help me my teachers pleasevery importient :

1-what is Expressed in radian measure, 235?

2-What is the value of sin(-240) ?

4-If the tangent of an angle is negative and its secant is positive, in which quadrant does the angle terminate?

5-In the unit circle shown at the right, what are the coordinates of B?

8-Which expression is not equivalent to sin 150 ?

9- A flower bed is planted in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length, in yards, of the border?

10-If sin (x + 20) = cos x ,what the value of x ?

12-The expression (1 + cos x)(1 - cos x) is equivalent to?

13-The expression cos 80 cos 70 + sin 80 sin 70   is equivalent to ?

15-The expression sin2A - 2sinA is equivalent to?

18-A sound wave is modeled by the curve y = 3sin4x. What is the period of this curve?
19-The graph of the function   y = 3sin(2x + )   will display a horizontal shift of ?

20-A radio transmitter sends a radio wave from the top of a 50-foot tower. The wave is represented by the graph shown at the right. What is the equation of this radio wave

21-Which graph represents the function f (x) = -sinx in the interval - < x < ?

22-Which value of x is not in the domain of the function defined by y = tanx ?

23-In ABC, m = 120, b = 10\", and c = 18\". What is the area of ABC to the nearest square inch?

24-In ABC, m = 45, m = 30, and a = 10. What is the length of side b?

25-You must cut a triangle out of a sheet of paper. The only requirements you must follow are that one of the angles must be 60, the side opposite the 60 angle must be 40 centimeters, and one of the other sides must be 15 centimeters. How many different triangle can you make?

26-In ABC, sinA = 0.5, m = 45, and b = 20. What is the length of side a?

27-Al is standing 50 yards from a maple tree and 30 yards from an oak tree in the park. His position is shown in the diagram at the right. If he is looking at the maple tree, he needs to turn his head 120 to look at the oak tree. How many yards apart are the two trees?

28-Find the exact value of sec 60 + cot 45 + csc 30 ?

31-prov the following identities.show complete solution:

1-sinØ+tanØ / cotØ+cscØ=sinØtanØ?

2-cotØ+tanØ=csc^2Ø+sec^2Ø / cscØ+secØ?

Solution

Solution:

- Expressed in radian measure, 235?

360 = 2 radians

1 = /180 radians

235 = 235/180 radians or 47/36 (factor down by 5)or approx 1.3 radians

-What is the value of sin(-240) ?

sin(-240 degrees) is the same as sin(120 degrees) (360 - 240 =120)

sin 120º = sin ( 90º + 30º )
sin ( + ß ) = sin cos ß + cos sin ß
sin ( 90º + 30º ) = sin 90º cos 30º + cos 90º sin 30º
..... ..... ..... ..... ... = ( 1 ) • ( 3 / 2 ) + ( 0 ) • ( 1/2 )
..... ..... ..... ..... ... = 3 / 2

-Value of sin 3pi/2+cos 2pi/3=?

sin(3pi/2)=-1
cos(2pi/3) = -cos(pi/3) = -1/2
-1-1/2 = -3/2

-If the tangent of an angle is negative and its secant is positive, in which quadrant does the angle terminate?

Secant is simply 1/cosine, so it\'s either I or IV. Tangent is negative, so it\'s either II or IV. Therefore, it\'s in IV.