{"id":1593,"date":"2019-02-14T00:33:16","date_gmt":"2019-02-14T00:33:16","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1593"},"modified":"2020-04-08T10:10:14","modified_gmt":"2020-04-08T10:10:14","slug":"sine-cosine-tangent","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2019\/02\/14\/sine-cosine-tangent\/","title":{"rendered":"Sine, Cosine, Tangent"},"content":{"rendered":"

[latexpage]<\/span><\/p>\n

Fun Math for Girls
\n<\/span>By Kelly Tan<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

Imagine you are in a field with trees, and the sun is shining above. You can learn a lot of math from here.<\/span><\/p>\n

Let\u2019s say that you walk a certain distance away from a tree (<\/span>x<\/span><\/i>) to point <\/span>A<\/span><\/i>. You were able to estimate the angle from the ground to the line that connects point <\/span>A<\/span><\/i> to the top to the tree (\u03b8) by using a large protractor. How would you find the height of the tree(<\/span>h<\/span><\/i>)? Do you measure it?<\/span><\/span><\/p>\n

\"\"<\/p>\n

You could measure it, but it would be very difficult and inefficient. Instead, you can use a math concept called the <\/span>tangent<\/span><\/i>. If you noticed, the lines <\/span>h<\/span><\/i>, <\/span>x<\/span><\/i>, and <\/span>L <\/span><\/i>make up a right triangle. The equation for tangent (short form is tan) is: $tan$\u03b8$ = \\frac{h}{x}$<\/span>. By multiplying <\/span>x<\/span><\/i> on both sides, you get $h = x tan$$\u03b8$.<\/span><\/span><\/p>\n

We can generalize the equation of tangent to: $tan$\u03b8$ = \\frac{opposite}{adjacent}$. Opposite is the leg of the triangle that is <\/span>opposite <\/span><\/i>to angle \u03b8. Adjacent is the leg of the triangle that is <\/span>adjacent<\/span><\/i>, or next to, angle \u03b8. You can tell the difference between the adjacent leg and the <\/span>hypotenuse<\/span><\/i>, because the adjacent always travels from angle \u03b8 to the $90^o$<\/span> angle of the triangle.<\/span><\/span><\/p>\n

\"\"<\/p>\n

There are 2 other equations that are useful for finding adjacent, opposite, or hypotenuse values, sine (sin) and cosine (cos). The equations are: $ sin$\u03b8$ = \\frac{opposite}{hypotenuse}$ and $cos$\u03b8$ = \\frac{adjacent}{hypotenuse}$.<\/span><\/p>\n

Sine, cosine, and tangent equations are <\/span>trigonometric equations<\/span><\/i>, which are very useful in trigonometry, a field of mathematics. Keep in mind that whenever you are calculating sine, cosine, or tangent, you have to be given an angle to solve the equation.<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

[latexpage] Fun Math for Girls By Kelly Tan Imagine you are in a field with trees, and the sun is shining above. You can learn a lot of math from here. Let\u2019s say that you walk a certain distance away from a tree (x) to point A. You were able to estimate the angle from […]<\/p>\n","protected":false},"author":1,"featured_media":1594,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1593","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/kellyfish.me\/wp-content\/uploads\/2019\/02\/field-with-long-grass-with-sky-and-clouds-and-trees-landscape-at-quincy-bluff-wisconsin.jpg?fit=5416%2C2512&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1593","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/comments?post=1593"}],"version-history":[{"count":5,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1593\/revisions"}],"predecessor-version":[{"id":1608,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1593\/revisions\/1608"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media\/1594"}],"wp:attachment":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media?parent=1593"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/categories?post=1593"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/tags?post=1593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}