# Math Destroyer Question

#### krnkimsung

5+ Year Member
Drawn from Practice Test # 9

25. Given: the sine of angle A is a negative number: One of teh two angles between 0 and 360 that A could be is 200. What is the other angle?

a. 20
b. 160
c. 340
d. 70
e. 290

The answer is 'c'

Thanks,

#### Maygyver

10+ Year Member
5+ Year Member
Is this one that uses the "CAST" nmeumonic for the quadrants? I know you can rule out a, b, and d because sin is going to be positive in those quadrants, but I forget how to work out that it is c and not e.

#### herkulease

10+ Year Member
What you're trying to find here is another angle with the same Sin, Cos value of whatever angle they want.

The short hand I learned was All students take calculus.

A is Quad I, everything is positive
S is Quad II, only Sin is positive, Cos is negative
T i s Quad III, sin and cos are both negative.
C is quad IV, Sin is negative Cos is positive.

for sin to be negative is has to be in quad III or IV. as maygyver noted that eliminates a, b, and d.

The reason why its C and not E is because of the reference angle that can be calculated.

For angles in Quad 1 the angle = its reference angle
quad 2 its 180-angle
quad 3 its angle - 180
quad 4 its 360 - angle

We are told that A is 200. that puts us in Quad III. So the reference angle would be 200 - 180 = 20.

The answer choices we have left puts us in the Quad 4. We already determined our reference angle. as 20.

So 360-X = 20. X would have to be 340.

sin 200 and sin 340 will both be -0.342

Sorry I know my explanation can be confusing so I'll try and simplify it below with an example

Cos 98 is - 0.139

Cos of what angle is also -0.139

98 degrees is in Quad 2. so to calculate the reference angle would be 180-98 = 82.

For Cos X to be a negative value it would have to be in Quad 3. We already have the reference angle so we just plug in the numbers and solve

So X - 180 = 82.

X = 262.

Try it out with a calculator and see what you get. You should get the same as Cos 98.

#### evanyou

7+ Year Member
Drawn from Practice Test # 9

25. Given: the sine of angle A is a negative number: One of teh two angles between 0 and 360 that A could be is 200. What is the other angle?

a. 20
b. 160
c. 340
d. 70
e. 290

The answer is 'c'

Thanks,
I usaully think the sine graph

you will have same value when the angle is 20 degree smaller to 360

cause 200 is 20 away from 180

FYI, by looking at the graph, we can deduce sin(200)=sin(340)=sin(-20)

enjoy my drawing

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#### Frederico Albin

##### Yes thats my bulldog :)
10+ Year Member
This problem is so simple...

sin is negative in quad3/4.
One of the angles is 200. Now you have to think of reference angles... It has to be in quad 4. 360-20=340... quad 4... all those other choices makes no sence what so ever...

#### dentalWorks

##### Nights Watchmen
7+ Year Member
This figure and explanation should help you out: