Using trigonometric identities to solve problems Video transcript i've already made a handful of videos that covers what I'm going to cover, the trigonometric identities I'm going to cover in this video. The reason why I'm doing it is that I'm in need of review myself because I was doing some calculus problems that required me to know this, and I have better recording software now so I thought two birds with one stone, let me rerecord a video and kind of refresh things in my own mind. So the trig identities that I'm going to assume that we know because I've already made videos on them and they're a little bit involved to remember or to prove, are that the sine of a plus b is equal to the sine of a times the cosine of b plus the sine of b times the cosine of a. That's the first one, I assume, going into this video we know.
History of trigonometry Hipparchuscredited with compiling the first trigonometric tablehas been described as "the father of trigonometry". The ancient Nubians used a similar method.
In BC, Hipparchus from NicaeaAsia Minor gave the first tables of chords, analogous to modern tables of sine valuesand used them to solve problems in trigonometry and spherical trigonometry. Centuries passed before more detailed tables were produced, and Ptolemy's treatise remained in use for performing trigonometric calculations in astronomy throughout the next years in the medieval ByzantineIslamicand, later, Western European worlds.
The modern sine convention is first attested in the Surya Siddhantaand its properties were further documented by the 5th century AD Indian mathematician and astronomer Aryabhata.
By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry. The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.
Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics.
It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series.
Trigonometric function In this right triangle: If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to degrees.
The two acute angles therefore add up to 90 degrees: The shape of a triangle is completely determined, except for similarityby the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle.
If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure: Sine function sindefined as the ratio of the side opposite the angle to the hypotenuse.Basic Trigonometric Ratios: Examples (page 2 of 2) List the values of sin (α), cos (α), sin (β), and tan (β) for the triangle below, accurate to three decimal places.
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Jun 18, · Simplify the ratio. Simplify answer and write answer as a fraction: 6 to ?
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Watch video · Sal reviews all the different trigonometric angle addition identities: sin(a+b), sin(a-c), cos(a+b), cos(a-b), cos(2a), and sin(2a). Review of trig angle addition identities.
And this is minus-- well, sorry. I just said you don't mix it up and then I mixed them up. Times the cosine of b minus sine of a times the sine of b.
Now, if you. Looking at our trig cheatsheet, we find an easy ratio where we can compare secant to 1. For example, secant to 1 (hypotenuse to horizontal) is the same as 1 to cosine: Suppose our secant is , i.e.
% of the radius of the unit circle.