Use identities to find values of the sine and cosine functions of the function for the angle measure a. theta, given that cos2theta=28/53 and 0theta < theta < 90degrees
b. 2theta, given sin theta= - sqrt 7 over 5 and cos theta > 0
c. 2x, given tan x=2 and cos x<0

Step-by-step explanation:

a) Given cos2theta=28/53 and 0degrees< theta < 90degrees

From cos2theta=28/53

b) Given

If cos theta 0, this means we need to look for the quadrant where sin is negative and cos is positive. That will be the fourth quadrant. In the fourth quadrant, theta = 360 - 31.95° = 328.05°

2theta = 2 * 328.05

2theta = 656.1°

c) Given tan x=2 and cos x<0, lets find the angle of x first.

If tan x = 2

x = tan^-1 2

x = 63.4°

Sine cos is less than 0, then we need to find the angle of x where tan is positive and cos is negative. That will be the third quadrant. In the third quadrant, ew value of x = 180+63.4

x = 243.4°

Since we are to find 2x,

2x = 2(243.4)

2x = 486.8°

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.