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Key ideas
Key ideas
The relationships between the length of the sides and the size of the angles in a triangle can be used to solve many problems involving position, distance, angles and area.
Equivalent measurement systems, such as degrees and radians, can be used for angles to facilitate ease of calculation.
Different representations of the values of trigonometric relationships, such as exact or approximate, may not be equivalent to one another.
The trigonometric functions of angles may be defined on the unit circle, which can visually and algebraically represent the periodic or symmetric nature of their values.
The sign of Sine, Cos and Tan
The sign of Sine, Cos and Tan
Discuss this table and find out the sign of cosine, sine and tangent in the various quadrants.
Negative and complementary angles
Negative and complementary angles
In your group, use the gadget below to figure out:
The relationship between the angle α (alpha) and its complementary angle (90-α). Describe these relationships in terms of sine and cosine eg: sine(α)=....
The relationships between the angle α and it's negative angle (-α). Describe sine(-α), cosine(-α) and tan(-α)
Well known angles and the exact values of Sin, Cos, Tan
Well known angles and the exact values of Sin, Cos, Tan
This video will help you remember the well known angles. there's a lot of logic in it!
https://www.youtube.com/watch?v=LN7aAp-ieyg
Using The Sine and Cosine rules (+ Ambiguous Case)
Using The Sine and Cosine rules (+ Ambiguous Case)
When using the sine function to find an unknown angle, your calculator not always will give you the answer you need. this isknown as the Ambiguous case. Examples are in the video.
Activity:
Activity:
The Ambiguous Case
The Ambiguous Case
How to remember the unit circle
How to remember the unit circle
This video gives memorization help for the unit circle with a trick, as well as a review of how to use the circle to find sin, cos, and tan. The cosine and sine values are the x and y coordinates of the unit circle points. To skip ahead:
1) For the ANGLES on the unit circle, skip to time 1:00.
2) For how to find COS (cosine function) values, skip to 4:18.
3) For the SIN (sine function) values, skip to 7:39.
4) For the COMPLETE UNIT CIRCLE chart explained, with all the points, and also when to use a NEGATIVE SIGN in some quadrants, skip to 8:17.
5) For DEGREES of the angles in the trig unit circle, skip to 10:50.
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