Answer:
1. y = 145
2. y = 145 and z = 215
3. y = 180 - x
4. y = 180 + x and z = 360 - x
5. y = 360 - x
6. y = 180 - x and z = 180 + x
Step-by-step explanation:
1. siny = sin35
Since sin35 is positive, siny is in the second quadrant.
So siny = sin(180 - 35) = sin35
siny = sin145 = sin35
Since siny = sin145, y = 145
2. cosy = cosz = -cos35
since -cos35 is negative in the second and third quadrant,
cosy = cos(180 - 35) = -cos35 and cosz = cos(180 + 35) = -cos35
cosy = cos145 = -cos35 and cosz = cos215 = -cos35
Since cosy = cos145 and cosz = cos215,
y = 145 and z = 215
3. If siny = sinx and x < 90,
since x < 90, sinx is in the first quadrant and siny is in the second quadrant since it is positive
siny = sin(180 - x) = sinx
Since siny = sin(180 - x)
y = 180 - x
4. siny = sinz = -sinx and x< 90
since -sinx is negative and sine is negative in the third and fourth quadrant respectively, siny and sinz are in the third and fourth quadrant,
siny = sin(180 + x) = -siny and sinz = sin(360 - x) = -sinx
Since siny = sin(180 + x) and sinz = sin(360 - x)
y = 180 + x and z = 360 - x
5. cosy = cosx and x < 90
Since cosx is positive in the first and fourth quadrant, and x is in the first quadrant,
cosy = cos(360 - x) = cosx
cosy = cos(360 - x)
y = 360 - x
6. cosy = cosz = -cosx and x< 90
since -cosx is negative in the second and third quadrant,
cosy = cos(180 - x) = -cosx and cosz = cos(180 + x) = -cosx
cosy = cos(180 - x) and cosz = cos(180 + x)
y = 180 - x and z = 180 + x
