Trigonometry the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.Learn More with Vidyabharti educational Institutions .
4. Sine FunctionSine Function
When you talk about the sin of an angle,
that means you are working with the
opposite side, and the hypotenuse of a
right triangle.
5. Sine functionSine function
Given a right triangle, and reference angle A:
sin A =
hypotenuse
opposite
A
opposite
hypotenuse
The sin function specifies
these two sides of the
triangle, and they must be
arranged as shown.
6. Sine FunctionSine Function
For example to evaluate sin 40°…
Type-in 40 on your calculator (make sure
the calculator is in degree mode), then
press the sin key.
It should show a result of 0.642787…
Note: If this did not work on your calculator,Note: If this did not work on your calculator,
try pressing thetry pressing the sinsin key first, then type-in 40.key first, then type-in 40.
Press the = key to get the answer.Press the = key to get the answer.
7. Sine Function
Try each of these on your calculator:
sin 55°
sin 10°
sin 87°
Sine FunctionSine Function
8. Sine Function
Try each of these on your calculator:
sin 55° = 0.819
sin 10° = 0.174
sin 87° = 0.999
Sine FunctionSine Function
9. Inverse Sine FunctionInverse Sine Function
Using sin-1
(inverse sin):
If 0.7315 = sin θ
then sin-1
(0.7315) = θ
Solve for θ if sin θ = 0.2419
Inverse Sine FunctionInverse Sine Function
10. Cosine function
The next trig function you need to know
is the cosine function (cos):
cos A =
hypotenuse
adjacent
A
adjacent
hypotenuse
Cosine FunctionCosine Function
11. Cosine Function
Use your calculator to determine cos 50°
First, type-in 50…
…then press the cos key.
You should get an answer of 0.642787...
Note: If this did not work on your calculator,
try pressing the cos key first, then type-in 50.
Press the = key to get the answer.
Cosine FunctionCosine Function
12. Cosine Function
Try these on your calculator:
cos 25°
cos 0°
cos 90°
cos 45°
Cosine FunctionCosine Function
13. Cosine Function
Try these on your calculator:
cos 25° = 0.906
cos 0° = 1
cos 90° = 0
cos 45° = 0.707
Cosine FunctionCosine Function
14. Using cos-1
(inverse cosine):
If 0.9272 = cos θ
then cos-1
(0.9272) = θ
Solve for θ if cos θ = 0.5150
Inverse Cosine FunctionInverse Cosine Function
15. Tangent function
The last trig function you need to know
is the tangent function (tan):
tan A =
adjacent
opposite
A
adjacent
opposite
Tangent FunctionTangent Function
16. Tangent FunctionTangent Function
Use your calculator to determine tan
40°
First, type-in 40…
…then press the tan key.
You should get an answer of 0.839...
Note: If this did not work on your
calculator, try pressing the tan key first,
then type-in 40. Press the = key to get the
answer.
17. Tangent Function
Try these on your calculator:
tan 5°
tan 30°
tan 80°
tan 85°
Tangent FunctionTangent Function
18. Tangent Function
Try these on your calculator:
tan 5° = 0.087
tan 30° = 0.577
tan 80° = 5.671
tan 85° = 11.430
Tangent FunctionTangent Function
19. Using tan-1
(inverse tangent):
If 0.5543 = tan θ
then tan-1
(0.5543) = θ
Solve for θ if tan θ = 28.64
Inverse Tangent FunctionInverse Tangent Function
20. Review
These are the only trig functions you will
be using in this course.
You need to memorize each one.
Use the memory device: SOH CAH TOA
adj
opp
A
hyp
adj
A
hyp
opp
A
=
=
=
tan
cos
sin
Review
21. Review
The sin function:
sin A =
hypotenuse
opposite
A
opposite
hypotenuse
22. Review
The cosine function.
cos A =
hypotenuse
adjacent
A
adjacent
hypotenuse
Review
23. Review
The tangent function.
tan A =
adjacent
opposite
A
adjacent
opposite
Review
26. Review
Solve for θ:
0.7987 = sin θ
0.9272 = cos θ
2.145 = tan θ
Review
27. What if it’s not a right triangle?
- Use the Law of Cosines:
The Law of Cosines
In any triangle ABC, with sides a, b, and c,
.cos2
cos2
cos2
222
222
222
Cabbac
Baccab
Abccba
−+=
−+=
−+=
28. What if it’s not a right triangle?
Law of Cosines - The square of the magnitude
of the resultant vector is equal to the sum of the
magnitude of the squares of the two vectors, minus two
times the product of the magnitudes of the vectors,
multiplied by the cosine of the angle between them.
R2
= A2
+ B2
– 2AB cosθ
θ