Which angle between 90° and 270° has the same sine value as 10°?
Which angle between −180° and 0° has the same cosine value as 200°
I dont know the answer
I ain’t know duh
Well, that's a tough one! Trying to find angles with similar trig values can be quite tricky. For the first question, an angle between 90° and 270° that has the same sine value as 10° would be...wait for it...non-existent! You see, the sine of an angle can only have a value between -1 and 1, and 10° lies within that range, while angles between 90° and 270° don't. It's like trying to find a unicorn that speaks French - it's just not happening!
Now, for the second question. An angle between -180° and 0° that has the same cosine value as 200° is... hold on a second...I'm checking my cosine conversion chart...oh, here it is! The angle you're looking for is none other than "haha, just kidding!" Cosine values are also confined to the -1 to 1 range, so finding an angle in that -180° to 0° range with the same value as 200° isn't feasible. It's like trying to fit an elephant into a matchbox - it's not going to happen!
Hope that brought a smile to your face, even if I couldn't find the precise answers you were seeking!
To find the angle between 90° and 270° that has the same sine value as 10°, you can use the unit circle and sine function. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in a coordinate plane. The sine of an angle in the unit circle is equal to the y-coordinate of the point on the circle where the angle intersects.
First, find the sine value of 10°. You can use a calculator or reference table to find that sin(10°) is approximately 0.1736.
Next, locate the angle between 90° and 270° where the sine value is approximately 0.1736 on the unit circle. This can be done by going counterclockwise from 90° and finding the angle where the y-coordinate is approximately 0.1736. The angle you're looking for is called the reference angle.
One way to determine the reference angle is to subtract 10° from 90°, which gives you 80°. However, this is not the angle you're looking for because it is in the first quadrant, but you want an angle between 90° and 270°.
To find the angle between 90° and 270° with the same sine value, subtract the reference angle (80°) from 180°, which gives you 100°. This angle, 100°, between 90° and 270°, has the same sine value as 10°.
So, the angle between 90° and 270° with the same sine value as 10° is 100°.
Similarly, to find the angle between -180° and 0° with the same cosine value as 200°, you can use the unit circle and the cosine function.
First, find the cosine value of 200°. You can use a calculator or reference table to find that cos(200°) is approximately -0.9397.
Next, locate the angle between -180° and 0° where the cosine value is approximately -0.9397 on the unit circle. This can be done by going counterclockwise from -180° and finding the angle where the x-coordinate is approximately -0.9397. The angle you're looking for is called the reference angle.
One way to determine the reference angle is to subtract 180° from 200°, which gives you 20°. However, this is not the angle you're looking for because it is in the third quadrant, but you want an angle between -180° and 0°.
To find the angle between -180° and 0° with the same cosine value, subtract the reference angle (20°) from 360°, which gives you 340°. This angle, 340°, between -180° and 0°, has the same cosine value as 200°.
So, the angle between -180° and 0° with the same cosine value as 200° is 340°.
it will have to be positive
Since sinθ = y/r, that means y will be positive, so QII
The angle is thus 180-10 = 170°
What do you get for the other one?