Solve 1/2 = sin theta, 0< theta< 180 degrees?
sin a = 1/2 <=>a = 30° + k360° ( k of Z ) <=>a = 180° - 30° + k360° <=>a = 30° + k360° <=>a = 150° + k360° 0° < a < 180° <=> 0° < 30° + k360° < 180° <=> -1/12 < k < 5/12 => k = 0 => a = 30° 0° < a < 180° <=> 0° < 150° + k360° < 180° <=> -5/12 < k < 1/12 => k = 0 => a = 150°
Sin theta = 5/13, 90 degrees The sine function is positive in the 1st and 2nd quadrants. If theta lies between 90 and 180 deg sin(theta) is positive, but cos(theta) and tan(theta) are negative. This constitutes a right-angled triangle, so cos (theta ) = -12/13 and tan(theta) = -5/12 You have to spot that 5, 12, 13 is a right-angled triangle. It is only because you are told that theta lies between 90 and 180 that the sine is positive and the other two are negative.
Sin (180 degrees - theta)?
sin(180° − θ) = sin(θ) It's an Identity expressing sine function in terms of its supplements.
Why sin 180 degree= 0 ?
Do you remember these => Sin of a degree = Opposite side / Hypotenuse Cos = Adjacent side / Hypotenuse. In a right angeled triangle, the line just opposite to your 90 angle is the hypotenuse and the line opposite for which you find the angle is the opposite angle and the third line is the adjacent. Think of a right angled triangle with one angle being 180. So the opposite side do not exist. So its lenght is 0. So Sine 180 = 0, as the numerator is 0
If 90 degrees < theta < 180 degrees and cos theta = -4/5, find sin 4theta. I have so much trouble with these type of questions. Help?
This may be a helpful site: https://bitly.com/trigiden Look at the double angle formulas: sin(2x) = 2*sin(x)*cos(x). If x = 2*theta,then sin(4theta) = sin(2x) = 2sin(x)cos(x) = 2sin(2theta)cos(2theta) = 2*[2*sin(theta)cos(theta)][1 – 2*sin²(theta)] = 4*sin(theta)cos(theta) – 8*sin³(theta)cos(theta) So now you have sin(4*theta) = 4*sin(theta)cos(theta) – 8*sin³(theta)cos(theta). Now what is sine(theta). Well we have a 3,4,5 right triangle. If cosine = 4/5, then sine = 3/5. With theta between 90° and 180°, sine will be positive and cosine negative. So we have 4*(3/5)*(-4/5) - 8*(3/5)³*(-4/5)
When does sin theta = 0?
For the best answers, search on this site https://shorturl.im/j4tAj 2sin(x)^2 + sin(x) = 0 sin(x) (2sin(x)+1) = 0 factor sin(x) out. Im using x instead of theta by the way sin(x) = 0 or 2sin(x) + 1 = 0 zero product property sin(x) is 0 at 0 and pi 2sin(x) + 1 = 0 sin(x) = -1/2 (simple algebra) sin(x) is -1/2 at (correct me if I am wrong) 7pi/6 and 11pi/6 You may want to check these two on a calculator but I'm pretty sure your answer is 0, pi, 7pi/6 and 11pi/6
Why does sin (180-theta) equal sin theta, with respect to the diagram?
Q posed:Why does sin (180-theta) equal sin theta, with respect to the diagram?I am going to offer another graph y = sin(θ), which, in conjunction with Philip’s unit circle diagrams, may help you understand the answer to your question:Point E has coordinates (θ, sin(θ)). Point F has co=ordinates (180-θ), sin(180-θ)).Notice that the sine values are the same – ie 0.5 – even though the angle measure are different, but related..: sin(θ) = sin(180-θ), for all values of θ, where 0 ≤ θ ≤ 180Hopefully this will help? Cheers! :)
How do I convert [math]\tan \theta[/math] to degree?
Haven’t understood your question fully, but taking a shot at it.You have [math]\tan \theta = 0.05670[/math]. So, [math]\theta[/math] (in radians) [math]= \tan^{-1} (0.05670).\ [/math]Assuming [math]-\frac{\pi}{2} < \theta < \frac{\pi}{2}[/math], we get [math]\theta = 0.056639[/math] radians (written as [math]0.056639^c[/math]).To convert from radians to degrees, we multiply the value in radians by [math]\frac{180}{\pi}.[/math]So, the value in degrees is[math]0.056639^c \times \frac{180}{\pi} \approx 3.2452^\circ.[/math]
How is pi equivalent to 180 degrees?
Pi doesn't equal any number of degrees because pi without a unit is just a number. The point is that pi radians is equal to 180 degrees.Radians are a unit of measurement for angles, just like degrees are, and pi is just the number of radians that makes up that angle. Just as one radian is equal to 57.3 degrees (approximately).Edit to include stuff from the comments.The best way to understand is to forget about degrees entirely. Degrees are not fundamental and radians were not designed to work nicely with degrees, they were designed to work nicely instead of degrees.Approach the problem as if there has never been a unit for measuring angles, and decide what the best way of doing it will be.The answer is that the best way of doing it is with a unit that splits the circle into 2pi parts.Why is this? Essentially because it makes trigonometry and many other bits of maths elegant. The example you give of sin is part of that. If we forget about degrees and we invent a new unit that makes things work nicely, we get radians