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bearn
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What are the step-by-step in solving these problems?
Country Boy said:For (1) I assume the lower left angle is a right angle.
Got it! Thank You so much!Country Boy said:For (2) the blue line is given by 6x+ 7y= 60 or y= -(6/7)x+ 60/7. Its slope is -6/7 so the "exterior angle" of that triangle is arctan(-6/7)= 139.4 degrees. The interior angle is 180- 139.4= 40.6 degrees. Since $\theta= 60$ degrees the third angle, where the red line crosses the base is 180- 60- 40.6= 120- 40.6= 79.4 degrees. So the slope of the red line is tan(79.4)= 5.34.
y= 5.34(x- x_0)+ y_0 where (x_0, y_0) is any point on the line. We are told that (3, 6) is such a point.
Trigonometric identities are equations that involve trigonometric functions, such as sine, cosine, and tangent, and are true for all values of the variables involved.
Trigonometric identities are important because they allow us to simplify complex trigonometric expressions and solve problems involving angles and sides of triangles.
The most commonly used trigonometric identities include the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities.
To prove a trigonometric identity, you must manipulate one side of the equation using algebraic and trigonometric properties until it is equivalent to the other side. This can involve using trigonometric identities, simplifying expressions, and substituting values for variables.
Trigonometric identities are used in a variety of fields, such as engineering, physics, and navigation, to solve problems involving angles and distances. They are also used in music and art to create visually appealing designs and patterns.