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  • Sine, Cosine and Tangent.

These bearings are shown on the diagram below. We see that the two lighthouses and the boat form a triangle.

Problem 201

Since we know the distance between the lighthouses and we have two angles we can use trigonometry to find the remaining two sides of the triangle, the distance of the boat from the two lighthouses. We can use the sine rule to find the missing lengths.

Solving a trig function with sine and cosine

If a triangle is given with two sides and the included angle known, then we can not solve for the remaining unknown sides and angles using the sine rule. We therefore investigate the cosine rule:.

List of trigonometric identities

The cosine rule relates the length of a side of a triangle to the angle opposite it and the lengths of the other two sides. Video: T. The distance the plane has to travel to get to Cape Town and hence the extra distance that the plane has had to travel due to the pilot's error. Such translations also occur when dealing with trigonometric functions, with a horizontal translation , or horizontal shift, being one of the most prominent transformations. From the sinusoidal equation, the horizontal shift is obtained by determining the change being made to the x- value.

The horizontal shift is C.

In mathematics, a horizontal shift may also be referred to as a phase shift. Horizontal shifts can be applied to all trigonometric functions. This expression is really where the value of C is negative and the shift is to the left.

Right Triangle

In this expression the value of C is positive and the shift is to the right. Note these different interpretations of " phase shift ". How to use your graphing calculator for graphing trig functions. NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.

Trigonometry/Graphs of Sine and Cosine Functions - Wikibooks, open books for an open world

The list of linear algebra problems is available here. Enter your email address to subscribe to this blog and receive notifications of new posts by email.

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