This lesson introduces and walks you through the basic concepts about the trigonometric functions and right triangle and their relationship. You will learn it with the
help of some examples and practice questions with solution, using video and explanations
in own handwriting by the instructor that brings in an element of realclass room
experience.(More text below video...)
(Continued from above)The values for the trigonometric functions are defined as the value that you get
when divided one side by the other side i.e. ratio of one side to the other. E.g.
sin x = opposite/hypotenuse. Further you'll look into how you can use the ratios of sidelength of right triangles
to determine the measures of sides and angles. We'll use the Pythagorean Theorem,
concept of ratio and properties of sines, cosines, and tangents to solve the triangle,
that is, to find unknown parts in terms of known parts. E.g. In a right triangle
ABC, with sides a, b and c, you need to remember:
Pythagorean Theorem: a^{2} + b^{2} = c^{2}
Sines: sin A = a/c, sin B = b/c
Cosines: cos A = b/c, cos B = a/c
Tangents: tan A = a/b, tan B = b/a
Now let us first find solution of a problem where we don't know the hypotenuse but
we do know the other two sides. Then proceed using the Pythagorean Theorem, and
that give us the hypotenuse. For example: if a = 10 and b = 24,
then
c^{2}
= a^{2} + b^{2} = 10^{2} + 24^{2}
= 100 + 576 = 676.
The square root of 676 is 26, so c = 26.
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