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Transcript of Trigonometric Functions
A function has an input and output. An example of a function is a trigonometric function. Can be used to determine any unknown side lengths of right angle triangles Some examples of trigonometric ratios that can be seen when looking at right angle triangles are: Sine = opposite/hypotenuse Cosine = adjacent/hypotenuse Tangent = opposite/Adjacent The Reciprocal Trigonometric Ratios: Cosecant = hypotenuse/Opposite Secant = hypotenuse/Adjacent Cotangent = Adjacent/Opposite Trigonometric functions are used to display the relationship between sides and angles in a triangle Trigonometric ratios are used when dealing with trigonometric functions Trigonometry has become very important in our everyday lives, as this function can be seen in natural phenomena The times of comet appearances can be calculated using trigonometric functions Trigonometric functions can also be used to model temperature changes and the movement of waves in water
Used in astronomy: at 6 month intervals, the Earth can be seen in proportion to another star from two corners, forming an isosceles triangle. The angle of this triangle formed can be determined using trigonometric functions. Airplane navigators use trigonometric functions Used in architecture Farmers Mathematicians Architects Computer Software Engineers Aerospace Engineers Surveying Technicians Every day Life Applications
Trigonometric functions help find unknown side lengths or angles in real life scenarios Studies the properties of triangles Music travels in sound waves. The music you listen to on your computer was first developed by sound engineers who studied sound waves, who developed the music using trigonometric laws. Trigonometry is seen in architecture, with the components of a building curved at certain angles to one another. The sine and cosine functions we learned about are seen in doctor’s offices, including CAT and MRI scanning. The next time you pay a visit to the doctor, take a look at how trigonometric functions keep us healthy and help us everyday!
Trigonometric Functions are essential for aircraft navigators. For example, trigonometric functions help us measure the height of mountains. This is important if you have a certain medical condition that does not allow you to travel at high altitudes. Trigonometry, meaning triangle measurement is an essential component in the field of mathematics Sine and cosine functions are important components of trigonometric functions, better known as sinusoidal functions This is known as a periodic sinusoidal function. A non periodic function does not have a cycle that repeats itself at regular intervals. An example of a non periodic function is a decaying exponential function f(t) = x sin(10t). 0.2t Trigonometry was developed in the third century B.C as an extended branch of geometry When first developed, focused on triangles and their measurements, angles and uses in everyday life Hipparchus was the first mathematician recorded to use the sine law when solving triangles A ferris wheel has a radius of 10 m and takes 40 seconds to complete one cycle. From the centre of the ferris wheel, the distance is 30 m above the ground. Determine the equation of the function. A ramp is being constructed for wheelchairs, measuring 10 m. The ramp makes a 60 angle with the ground and a 90 angle at the peak, where the ramp and top intersect. Find the width of the ramp. We know that cos60 = 1/2 because it is a special angle. 0 cos60 = adjacent/hypotenuse
1/2 = adjacent/10 m
10 m x 1/2 = adjacent
5 m = adjacent
Therefore the width is 5 m. Both of these problems show how one could use trigonometric functions in real life applications. a = radius, 10 m
c = 30 m
Period = 40 seconds
k = 360/40
k = 9
d = 40/4
d = 10 y = 10sin9 (t - 10) + 30
y = 10cos (9t-90-90) +30
y = 10cos (9t-180) +30
y = 10cos9 (t-20) +30 This function is periodic because there is a pattern of y values that repeats itself at regular intervals. This function is sinusoidal because it is periodic with smooth waves. y = sinx y = cosx 0 Simply put? Trigonometric functions are EVERYWHERE and are important to everyday aspects in our daily lives! 0 0 min = c - a
min = 30 - 10
min = 20
max = c + a
max = 30 + 10
max = 40