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Trigonometry

T1.1 and T1.2. Trigonometry. To convert from degrees to radians multiply by Example: Convert 155 deg to radians Notice how the units cancel to leave radians!. Section T1.1 - Angle Conversion. To convert from radians to degrees multiply by Example: Convert radians to degrees

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Trigonometry

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  1. T1.1 and T1.2 Trigonometry

  2. To convert from degrees to radians multiply by • Example: Convert 155 deg to radians • Notice how the units cancel to leave radians! Section T1.1 - Angle Conversion

  3. To convert from radians to degrees multiply by • Example: Convert radians to degrees • Notice how the units cancel to leave degrees! Section T1.1 - Angle Conversion

  4. Section t1.1 - Table of Common angles It is important to know how to convert between degrees and radians, as in the last slide. However, the angles on this slide are common angles and should be memorized!

  5. Use the formula where r is the radius and is in radians. • Memorize this formula! • Example: Find the length of the arc of the circle with radius 15 cm intercepted by an angle of measure 35˚. • First convert to radians: • Now find arc length Section t1.1 - Finding arc length

  6. You are also responsible to know • How to draw angles in standard position • How to find coterminal angles • Definition of supplementary and complementary • You do not need to know • Area of a sector • Degrees, minutes, seconds • Word problems What else is in section T1.1??

  7. SOH CAH TOA!! SOH CAH TOA Section t1.2 – right triangle trig hypotenuse opposite θ adjacent

  8. Section t 1.2 – six trig functionS Reciprocal Reciprocal Reciprocal

  9. Example – find the six trig functions for angle θ Section t 1.2 – six trig functionS (hypotenuse) 6 (opposite) θ 10 (adjacent)

  10. 45-45-90˚ right triangle * memorize!! Use SOH CAH TOA on this triangle to find the trig functions for 45˚. Section t 1.2 – special right triangles 45˚ 1 45˚ 1

  11. 30-60-90˚ right triangle * memorize!! Use SOH CAH TOA on this triangle to find the trig functions for 30 ˚ and 60˚. Section t 1.2 – special right triangles 30˚ 2 60˚ 1

  12. See pages 21-23 of Trig Supplement text for summary of values for the special right triangles. Please remember to check the MODE of your calculator when finding the values of each trig function. You should switch between radian and degree modes where necessary. Section t 1.2 – special right triangles

  13. Solving a right triangle means finding the length of each side and the measure of each angle. • Example. Given θ=A=55˚, b=4 ft , solve the triangle. • B=180 – 90 – 55 = 35˚ • tan 55 =a/4 a = 4*tan55=5.71 ft • cos 55= 4/c c=4 / cos (55) = 6.97 • Or use Pythagorean theorem for c: Section t1.2 – solving a triangle B c a 55 4

  14. Angle of elevation Angle of depression Section t1.2 - Angles of elevation & depression Example: A bird is sitting on top of a television antenna which casts a shadow that is 75.0 m long. If the angle of elevation of the sun is 39 degrees, calculate how high above the ground the bird is perched. Angle of elevation horizontal  Solution: Note you have info about the opposite and adjacent side for the given angle. So use tangent. x horizontal Angle of depression 39˚ 75 m tan 39 = x/75 x=75 tan 39 x≈60.7 m

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