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More Trigonometry
Karten in diesem Stapel (14)
- 1What steps should we take in order to solve something like sinx = 0.5 ?1. Check calculator is in right format (deg)
2. Find principle value (so sin-1 of 0.5)
3. Find other possible answers using appropriate method - 2What 2 methods can we use to find other possible answers?1. Graph method
2. CAST method - 3How do we do the graph method?1. Draw corresponding trigonometric graph
2. Plot the point of the principle value previously found
3. Minus 180 from this value to get the another value (as symmetrically equal)
4. Now add and subtract 360 from both these values and check the answers are within the range (if not, ignore) - 4How do we do the CAST method?1. Draw bow-tie on graph with CAST and degrees
2. Put the principle value in each quadrant near the centre of the bow-tie (all same)
3. See which quadrant your trig function is positive, and subtract the corresponding angle from the principle value.
4. Find other values (e.g. add/subtract 360, invert sign or add/subtract 180) - 5If we have 60 and 300 degrees from cos, what are the 2 other values?-60 and -300 degrees
- 6If we have tanx=1 , and tan-1(1)=45, how would we find all values between -360 and 360-315 , -135 , 45 , 225
(as period of tan=180, so add/subtract 180) - 7Solve: sinx = root(2) / 2 , range between -360 and 180sin-1(root(2) / 2) = 45
Use sine graph: 180-45 = 135
45-360 = -315 , 45+360 = 405 (ignored)
135-360 = -225 , 135+360 = 495
So answers are 45, 135, -315 and -225 - 8Solve: sinx=-1/2 , range between 0 and 360sin-1(-1/2) = -30
Use sine graph:-180 - -30 = -150
-150+360 = 210 , -30+360 = 330
Answers: -30 , -150 , 210, 330 - 9Solve: cosx= -root(3) / 2 , range between -360 and 360cos-1(-root(3) / 2) = 150
Use cos graph: 360-150=210
Answers: 150 , 210 , -150 , -210 - 10What is the sine rule?a/sinA = b/sinB = c/sinC
- 11If we are missing an angle and we want to use the sine rule, how could we make it easier?Change to: sinA/a = sinB/b = sinC/c
- 12What is the cosine rule in terms of a^2 ?a^2 = b^2+c^2 - 2bcCosA
- 13What is the cosine rule in terms of cosA ?cosA = (b^2+c^2-a^2)/2bc
- 14If we get an acute angle using the sine rule when the angle looks obtuse, what should we do?180 - answer