Negative 1, right? So x is going to be greater X, and I'm saying that that is equal to theta, what's theĭomain restricted to? What are the valid values of x? x could be equal to what? Well if I take the sine ofĪny angle, I can only get values between 1 and Side note, what's its domain restricted to? So if I'm taking theĪrcsine of something. Just restrict its range to the most natural place. Valid function- In order for the inverse sine function toīe valid, I have to restrict its range. It maps to pi over 4 plus 2 pi or pi over 4 plus 4 pi. Of x, where it maps to multiple values, right? Where it maps to pi over 4, or If I take the function- I can't have a function, f Of them, you would get square root of 2 over 2. Would think, would be valid answers for this, right? Because if you take the sine ofĪny of those angles- You could just keep adding 360 degrees. The unit circle, right? And you'd be correct. And all of those would workīecause those would all get me to that same point of But I could just keep addingģ60 degrees or I could keep just adding 2 pi. That gives me, when I take the sine of that angle that Review, I'm giving you a value and I'm saying give me an angle This as, the arcsine- sorry -arcsine of the square root ofĢ over 2 is equal to pi over 4. ![]() So my question mark isĮqual to pi over 4. The sine of pi over 4 is equal to square root of 2 over 2. The sine of pi over 4 is square root of 2 over 2. Root of 2 over 2? Well I just figured out that Statements as saying sine of what is equal to the These statements as saying square- Let me do it. Would I have to take the sine of in order to get square Square root of 2 over 2? All this is asking is whatĪngle would I have to take the sine of in order to get the This could have just as easilyīeen written as: what is the inverse sine of the Sometimes referred to as the inverse sine. When they have this word arc in front of it- This is also Sine of an angle is, but this is some new trigonometricįunction that Sal has devised. Please tell me what the arcsine of the square Let's say on another day, I come up to you and I say you, The sine of this, is just this height right here. This distance too, it would also be the same thing. I can put that in rational formīy multiplying that by the square root of 2 over 2. Of 1/2, which is one over the square root of 2. Plus x squared is equal to 1 squared, which is just 1. Triangle, right? Their base angles are the same. Let me draw the triangleĪ little bit larger. You would draw thatĪs a y-coordinate on the unit circle. Radians, which is the same thing as 45 degrees. Looking unit circle, but you get the idea. Or you would draw the unit circle right there. ![]() To write that thick -please tell me what sine The street and say you, please tell me what- so I didn't want Pi/6 is the radian measure that has a sine value of 1/2. So it just depends on the question.Īrcsin(1/2) = pi/6 for example. A lot of questions will ask you the arcsin(4/9) or something for example and that would be quite difficult to memorize (near impossible). ![]() It takes some time working with it, but it can be done. If it's all simple degree or radian measurements that you are working with, then yes, it can be memorized. The same logic follows for arctan and arc cos.ģ) Well, it's set at -90 degrees to 90 degrees.Ĥ) Somewhat. But, if you take quadrants 1 and 4, then the sin function hits all possible values. In quadrants 1 and 2 sin will have the same value. ![]() There's nothing wrong with the original answer of 1/sqrt(2), but this is just more 'proper', if you will.Ģ) Arcsin is restricted to the 1st and 4th quadrant because the value of sine goes from all possible values that way. That's why he calls it rational form and multiples by sqrt(2)/sqrt(2). It is sometimes more practical and cleaner to find a way to get the square root out of the dominator. When evaluating the composition of a trigonometric function with an inverse trigonometric function, you may use trig identities to assist in determining the ratio of sides.1) A lot of teachers do not like seeing square roots in the denominator.When evaluating the composition of a trigonometric function with an inverse trigonometric function, draw a reference triangle to assist in determining the ratio of sides that represents the output of the trigonometric function.
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