{"id":66963,"date":"2018-06-27T18:31:24","date_gmt":"2018-06-27T18:31:24","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=66963"},"modified":"2018-06-27T18:32:38","modified_gmt":"2018-06-27T18:32:38","slug":"intro-to-trigonometry-sine-cosine-and-tangent","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2018\/06\/27\/intro-to-trigonometry-sine-cosine-and-tangent\/","title":{"rendered":"Intro To Trigonometry: Sine, Cosine, and Tangent"},"content":{"rendered":"

Sin, cos, and tan are three functions that each provide a relationship between two sides and one angle of a right-angled triangle – that is, a triangle with a 90\u00b0 angle.<\/span><\/p>\n

If we have some right angled triangle, we can mark one one the two acute angles with an X, and label the sides in the following way:<\/span><\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

The side across from the right angle is the Hypotenuse. This is also the longest side.\u00a0<\/span>The side next to the angle X that is not the Hypotenuse is the Adjacent side. \u201cAdjacent\u201d means \u201cnext to.\u201d\u00a0<\/span>The side across from the X is the Opposite side.<\/span><\/p>\n

We then have the following relations:<\/span><\/p>\n

sin X = Opposite \/ Hypotenuse<\/span><\/p>\n

cos X = Adjacent \/ Hypotenuse<\/span><\/p>\n

tan X = Opposite \/ Adjacent<\/span><\/p>\n

One way to remember these relations is with the acronym SOH CAH TOA.\u00a0<\/span>These equations are useful for finding side lengths and the values of angles.<\/span><\/p>\n

Finding Sides<\/b><\/h3>\n

In the above example, if:<\/span><\/p>\n

Adjacent = 10<\/span><\/p>\n

X = 45\u00b0<\/span><\/p>\n

Then we can say<\/span> tan 45\u00b0 = Opposite \/ 10.\u00a0<\/b>Solving the equation for the Opposite side, we get:<\/span><\/p>\n

1 = Opposite \/ 10<\/span><\/p>\n

10 = Opposite<\/span><\/p>\n

And we have that the length of the Opposite side is 10 units.\u00a0<\/span><\/p>\n

We could also say that <\/span>cos 45\u00b0 = 10\/ Hypotenuse.\u00a0<\/b>Solving this equation for the Hypotenuse, we get:<\/span><\/p>\n

 <\/p>\n

0.7071 = 10 \/ Hypotenuse<\/span><\/p>\n

Hypotenuse * 0.7071 = 10<\/span><\/p>\n

Hypotenuse = 10 \/ 0.7071<\/span><\/p>\n

Hypotenuse = 14.14<\/span><\/p>\n

And we have that the length of the Hypotenuse is 14.14 units.<\/span><\/p>\n

Finding Angles<\/b><\/h3>\n

We can also use the sin, cos, and tan relationships to find angle values if we know the lengths of two or more sides.<\/span><\/p>\n

In the above example, if:<\/span><\/p>\n

Opposite = 15<\/span><\/p>\n

Hypotenuse = 30<\/span><\/p>\n

Then we can say<\/span> sin X = 15 \/ 30.\u00a0<\/b>Solving for X, we get:<\/span><\/p>\n

sin X = 0.5<\/span>\"\"<\/a>X = 30\u00b0<\/span><\/p>\n

And we have that X is an angle of 30\u00b0.<\/span><\/p>\n

\"\"<\/a><\/p>\n

Hopefully this guide helped you to gain a better understanding of how to use sin, cos, and tan!<\/b><\/p>\n

Interested in math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/a>\u00a0<\/span>is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in New Haven, CT: visit: Tutoring in Alpharetta, GA.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Sin, cos, and tan are three functions that each provide a relationship between two sides and one angle of a right-angled triangle – that is, a triangle with a 90\u00b0 angle. If we have some right angled triangle, we can mark one one the two acute angles with an X, and label the sides in […]<\/p>\n","protected":false},"author":17,"featured_media":66967,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-66963","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=66963"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/66963\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media\/66967"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=66963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=66963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=66963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}