Redefining Sine (3 of 3: Angles Greater Than 90°)

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[@TheMaverickanupam]

That was magnificent

[@torizaemon]

Good lesson. I understood it.

[@ssthu3311]

Thanks a lot Sir

[@anamayapnambiar]

Thank you sir, my school didn't taught this part and i was confused how sine 180 can exit 😊🙏 now im all good 👍🏻

[@Professor_7O]

How we can apply pythagorean theorem in the case of non 90 angles?

[@jannatulnyeemratul6039]

Sir,Why is sin of the reference angle equal to sin of the original angle?I would be grateful if you answer.

[@ethanthean1952]

The values of sin function is defined by the y-value on the unit circle. The sin of the reference angle is equal to sin of the original angle because a circle is symmetrical across the x- and y-axes. Any angle in the first quadrant (0 to 90 degrees) can be flipped across the x- and y- axes to give the same length (but different +ve or -ve signs) and same angle. Trig ratios (sin, cos, tan) were previously limited to values between 0-90 degrees in a right angle triangle. But these trig ratios (sin, cos, tan) become trig functions (take on any real number value from 0 to 360) on a unit circle. But because the unit circle is a circle, any values greater than 360 or less than 0 will just repeat itself on the circle. So the trig functions can take on any real number from -infinity to +infinity and give you a value (x-coordinate for cos, y-coordinate for sin, the gradient or slope for tan). The sin, cos, tan values that calculators are programmed with, comes from the x-values, y-values, slope of the coordinates on the unit circle.

[@zhaotongzhang5834]

Where you are teaching? Which school?